COMPARISON OF DESIGN SPECIFICATIONS

FOR

SEISMICALLY ISOLATED BUILDINGS

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF

MIDDLE EAST TECHNICAL UNIVERSITY

BY

EMRE ACAR

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR

THE DEGREE OF MASTER OF SCIENCE

IN

CIVIL ENGINEERING

FEBRUARY 2006

Approval of the Graduate School of Natural and Applied Sciences

Prof. Dr. Canan Özgen Director

I certify that this thesis satisfies all the requirements as a thesis for the degree of

Master of Science.

Prof. Dr. Erdal Çokca Head of Department

This is to certify that we have read this thesis and that in our opinion it is fully

adequate, in scope and quality, as a thesis for the degree of Master of Science.

Assoc. Prof. 'U��8÷XUKDQ�$N\�]� Supervisor

Examining Committee Members

Prof. Dr. S. Tanvir Wasti (METU, CE)

Assoc.�3URI��'U��8÷XUKDQ�$N\�] (METU, CE)

Assoc. Prof. Dr. Ahmet Yakut (METU, CE)

Asst. Prof. Dr. Ahmet Türer (METU, CE)

M.Sc. Mevlüt Kahraman �d(9ø./(5�ø1ù$$7�

iii

I hereby declare that all information in this document has been obtained and

presented in accordance with academic rules and ethical conduct. I also declare

that, as required by these rules and conduct, I have fully cited and referenced

all material and results that are not original to this work.

Name, Last name: Emre Acar

Signature :

iv

ABSTRACT

COMPARISON OF DESIGN SPECIFICATIONS

FOR SEISMICALLY ISOLATED BUILDINGS

Acar, Emre

M. Sc., Department of Civil Engineering

6XSHUYLVRU��$VVRF��3URI��'U��8÷XUKDQ�$N\�]

February 2006, 103 pages

This study presents information on the design procedure of seismic base isolation

systems. Analysis of the seismic responses of isolated structures, which is oriented to

give a clear understanding of the effect of base isolation on the nature of the

structure; and discussion of various isolator types are involved in this work.

Seismic isolation consists essentially of the installation of mechanisms, which

decouple the structure, and its contents, from potentially damaging earthquake

induced ground motions. This decoupling is achieved by increasing the horizontal

flexibility of the system, together with providing appropriate damping. The isolator

increases the natural period of the overall structure and hence decreases its

acceleration response to earthquake-generated vibrations. This increase in period,

v

together with damping, can reduce the effect of the earthquakes, so that smaller loads

and deformations are imposed on the structure and its components.

The key references that are used in this study are the related chapters of FEMA and

IBC2000 codes for seismic isolated structures. In this work, these codes are used for

the design examples of elastomeric bearings. Furthermore, the internal forces

develop in the superstructure during a ground motion is determined; and the different

approaches defined by the codes towards the ‘scaling factor’ concept is compared in

this perspective.

Keywords: Seismic Isolation, Base Isolation, Earthquake Resistant Design, Seismic

Protective Systems

vi

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viii

Dedicated to my parents, Güler and Eyüp Acar,

for their presence and encouragement.

ix

ACKNOWLEDGMENTS

I would like to express my sincere gratitude to the following:

Assoc. Prof. Dr. 8÷XUKDQ Akyüz, my thesis supervisor, for his proper directives and

close interest without which this work would never be realized,

My family for their ineffable guidance, motivation and constant support,

Finally, my love, Özlem øOKDQ, for patiently enduring and sharing the years of

preparation with me.

x

TABLE OF CONTENTS

PLAGIARISM.........………………………………………………………………… iii

ABSTRACT…………………………………………………………………………. iv

ÖZ……………………………………………………………………………………vi

ACKNOWLEDGEMENTS…………………………………………………………. ix

TABLE OF CONTENTS…………………………………………………….……… x

LIST OF FIGURES……………………………………………………………...… xiii

LIST OF TABLES………………………………………………………......…..…..xvi

LIST OF SYMBOLS............................................................................................... xviii

CHAPTER

1. INTRODUCTION…………………………………………………… 1

1.1 Principles of Seismic Isolation……………………..………….. 2

1.2 Seismic Isolation Systems……………………………………... 4

1.2.1 Elastomeric Bearings…………………………………. 4

1.2.1.1 Low Damping Natural and Synthetic

Rubber Bearings…………………………….. 4

1.2.1.2 High Damping Natural Rubber Bearings…… 5

1.2.1.3 Lead-Plug Bearings…………………………. 6

1.2.2 Isolation Systems Based on Sliding…………………...7

1.2.2.1 Pure-Friction System……………………….. 8

1.2.2.2 Resilient-Friction Base Isolation System…... 8

1.2.2.3 Electric de France System………………….. 9

1.2.2.4 Friction Pendulum System………………... 10

1.3 Current Applications…………………………………………. 11

xi

1.4 Literature Survey....................................................................... 14

1.5 Aims and Scope………………………………………………. 16

2. MATHEMATICAL MODELLING OF ISOLATORS…………….. 17

2.1 Mechanical Characteristics of Elastomeric Isolators................. 17

2.1.1 Comparison of Compression Modulus……………... 18

2.2 Equivalent Linear Model of Isolators……...................……… 21

2.3 Bilinear Model of Isolators…………………………………... 22

2.4 Comparison of Response for Bilinear and

Equivalent Linear Model…………………………………….. 24

3. CASE STUDIES…………………………………………………… 37

3.1 Introduction………………………………………………….. 37

3.2 Description of the Structures………………………………… 37

3.2.1 Three-Storey Symmetrical Building (Type-I)……… 38

3.2.2 Five-Storey Symmetrical Building (Type-II)……….. 39

3.2.3 Eight-Storey Symmetrical Building (Type-III)…....... 40

3.2.4 Non-symmetrical Building (Type-IV)…………........ 40

3.3 Analysis Methods…………………………………………….. 42

3.3.1 Static Equivalent Lateral Force Procedure…............. 42

3.3.2 Response Spectrum Analysis……………………….. 45

3.3.3 Time History Analysis……………………………… 46

3.4 Design Codes………………………………………………… 46

3.4.1 IBC2000…………………………………………….. 47

3.4.2 FEMA273…………………………………………... 49

4. ISOLATION SYSTEM DESIGN....................................................... 50

4.1 Design of High Damping Rubber Bearing................................ 50

4.1.1 Lateral Stiffness of Base Isolators............................... 51

4.1.2 Estimation of Lateral Displacements……………….. 52

4.1.3 Estimation of Disc Dimensions…………………….. 52

4.1.4 Actual Bearing Stiffness & Revised

Fundamental Period………………………………… 53

4.1.5 Bearing Detail………………………………………. 53

xii

4.1.6 Buckling Load……………………………………… 55

4.2 Performance Comparison of Isolation Systems…….………... 56

5. ANALYSIS AND DISCUSSION OF RESULTS.............................. 61

5.1 Analysis of the Base Isolated Symmetrical Building………... 61

5.1.1 Scaling of the Results ………….....................……… 61

5.1.1.1 Scaling for Static Equivalent Lateral

Force Procedure …………...………………. 62

5.1.1.2 Scaling for Response Spectrum Analysis...... 63

5.1.1.3 Scaling for Time History Analysis................ 65

5.1.2 Results of the Analyses …….................…………….. 67

5.2 Analysis of the Base Isolated Non-symmetrical Building…… 80

5.2.1 Scaling of the Results ………….....................……… 80

5.2.1.1 Scaling for Static Equivalent Lateral

Force Procedure …………...………………. 80

5.2.1.2 Scaling for Response Spectrum Analysis...... 81

5.2.1.3 Scaling for Time History Analysis................ 83

5.2.2 Results of the Analyses................................................ 84

5.3 Comparison of FEMA and IBC2000…………............……… 94

5.3.1 Equivalent Lateral Load Analysis………………….. 95

5.3.2 Response Spectrum Analysis……………………….. 95

5.3.3 Time History Analysis……………………………… 96

6. CONCLUSION…………………………………………………….. 99

REFERENCES……………………………………………………………………..101

xiii

LIST OF FIGURES

FIGURES Page

1.1 Acceleration response spectrum……………………………………………... 2

1.2 Displacement response spectrum…………………………………………….. 3

1.3 High damping rubber bearing………………………………………………... 6

1.4 Lead-Plug bearing……………………………………………………………. 7

1.5 Resilient-friction base isolation system……………………………………… 9

1.6 Friction pendulum system…………………………………………………... 11

2.1 Ec – S relationship…………………………………………………………... 20

2.2 Ec – G relationship………………………………………………………….. 20

2.3 Ec – K relationship………………………………………………………….. 21

2.4 Force displacement relationship of equivalent linear model........................... 22

2.5 Force displacement relationship of bilinear model…………………………. 23

2.6 Acceleration spectra………………………………………………………… 24

2.7 Displacement spectra……………………………………………………….. 25

2.8 Time variation of top floor acceleration under the effect of

Imperial Valley 1979 earthquake…………………………………………… 29

2.9 Time variation of bearing displacement under the effect of

Imperial Valley 1979 earthquake…………………………………………… 30

2.10 Time variation of top floor acceleration under the effect of

Kocaeli 1999 earthquake………………………………………………….… 31

2.11 Time variation of bearing displacement under the effect of

Kocaeli 1999 earthquake…………………………………………………… 32

2.12 Time variation of top floor acceleration under the effect of

Loma Prieta 1989 earthquake………………………………………………. 33

2.13 Time variation of bearing displacement under the effect of

Loma Prieta 1989 earthquake………………………………………………. 34

xiv

2.14 Force-deformation behavior for Imperial Valley Earthquake

(bilinear hysteretic models)…......................……………………………….. 35

2.15 Force-deformation behavior for Kocaeli Earthquake

(bilinear hysteretic models)…......................……………………………….. 35

2.16 Force-deformation behavior for Loma Prieta Earthquake

(bilinear hysteretic models)…......................……………………………….. 36

3.1 Plan view of symmetrical building types…………….……………………... 38

3.2 Section view building Type-I………................................…...…………….. 39

3.3 Section view of building Type-II.................................................................... 39

3.4 Section view of building Type-III................................................................... 40

3.5 Plan view of building Type-IV........................................................................ 41

3.6 Section views of building Type-IV..................................................................41

3.7 Plan dimensions for calculation of DTD…………………………………….. 44

3.8 Response spectrum functions given in Turkish Seismic Code……………... 44

4.1 Detail design of isolator…………………………………………………….. 55

4.2 Effect of damping for equal base shear case……………………………….. 58

4.3 Effect of damping for equal period case……………………………………. 59

4.4 Effect of damping for equal displacement case…………………………….. 60

5.1 Base shear in X direction (Type-II, time history analysis).............................. 73

5.2 Base shear in Y direction (Type-II, time history analysis).............................. 74

5.3 Base moment in X direction (Type-II, time history analysis)......................... 74

5.4 Base moment in Y direction (Type-II, time history analysis)......................... 75

5.5 Maximum interstory drift ratio (Type-II, time history analysis)..................... 76

5.6 Base shear in X direction (Type-II, response spectrum analysis)................... 76

5.7 Base shear in Y direction (Type-II, response spectrum analysis)................... 77

5.8 Base moment in X direction (Type-II, response spectrum analysis)............... 78

5.9 Base moment in Y direction (Type-II, response spectrum analysis)............... 78

5.10 Maximum interstory drift ratio (Type-II, response spectrum analysis)........... 79

5.11 Base shear in X direction (Type-IV, time history analysis)............................ 88

5.12 Base shear in Y direction (Type-IV, time history analysis)............................ 89

5.13 Base moment in X direction (Type-IV, time history analysis)....................... 89

5.14 Base moment in Y direction (Type-IV, time history analysis)........................ 90

xv

5.15 Maximum interstory drift ratio (Type-IV, time history analysis)....................91

5.16 Base shear in X direction (Type-IV, response spectrum analysis).................. 91

5.17 Base shear in Y direction (Type-IV, response spectrum analysis).................. 92

5.18 Base moment in X direction (Type-IV, response spectrum analysis)............. 93

5.19 Base moment in Y direction (Type-IV, response spectrum analysis)............. 93

5.20 Maximum interstory drift ratio (Type-IV, response spectrum analysis)......... 94

xvi

LIST OF TABLES

TABLES Page

1.1 Current applications of seismic isolation…………………………………… 13

2.1 The parameters of bilinear hysteresis loop…………………………………. 26

2.2 Results of the analyses..................................................................................... 27

3.1 Damping coefficient………………………………………………………... 42

3.2 Ground motions used in time history analyses................................................ 46

3.3 Scaling limits for IBC2000.............................................................................. 49

5.1 Calculation of scaling factor for Type-II according to IBC2000.................... 62

5.2 Fixed and isolated periods of buildings........................................................... 63

5.3 Calculation of scaling factor for Type-I according to IBC2000...................... 64

5.4 Calculation of scaling factor for Type-II according to IBC2000.................... 64

5.5 Calculation of scaling factor for Type-III according to IBC2000................... 64

5.6 Calculation of scaling factor for Type-I according to FEMA......................... 65

5.7 Calculation of scaling factor for Type-II according to FEMA........................ 65

5.8 Calculation of scaling factor for Type-III according to FEMA....................... 65

5.9 Calculation of scaling factor for Type-II according to IBC2000.................... 66

5.10 Calculation of scaling factor for Type-II according to FEMA........................ 67

5.11 Results of the analyses for Type-II.................................................................. 68

5.12 Comparison Table for Type-II......................................................................... 69

5.13 Results of time history analysis for each earthquake record, Type-II............. 70

5.14 Calculation of scaling factor for Type-IV according to IBC........................... 79

5.15 Fixed and isolated periods............................................................................... 79

5.16 Calculation of scaling factor for Type-IV according to IBC2000................... 80

5.17 Calculation of scaling factor for Type-IV according to FEMA...................... 81

xvii

5.18 Calculation of scaling factor for Type-IV according to IBC2000................... 82

5.19 Calculation of scaling factor for Type-IV according to FEMA...................... 82

5.20 Results of the analyses for Type-IV................................................................ 83

5.21 Comparison Table for Type-IV....................................................................... 84

5.22 Results of time history analysis for each earthquake record, Type-IV............85

xviii

LIST OF SYMBOLS

A Cross-sectional area

A0 Seismic zone coefficient

BD Numerical coefficient for effective damping at design displacement

b Long side length of building in plan

D Specified design displacement

Dy Yield displacement

DD Displacement corresponding to the ‘design earthquake’

DTD Total design displacement

DM Displacement corresponding to the ‘max. capable earthquake’

d Short side length of building in plan

e Eccentricity

Eloop Energy dissipation per cycle of loading

Ec Instantaneous compression modulus

F+

Positive force at test displacement

F –

Negative force at test displacement

(Fv)max Maximum vertical load for one isolator

G Shear modulus of the elastomer

g Acceleration of gravity

h Total height of bearing

hi Height above the base to level i

hx Height above the base to level x

I Importance factor of structure

KH Horizontal stiffness of bearing

xix

KV Vertical stiffness of bearing

K Bulk modulus

K1 Elastic stiffness

K2 Post-yield stiffness

keff Effective stiffness

kD Lateral stiffness corresponding to the ‘design earthquake’

kM Lateral stiffness corresponding to the ‘max. capable earthquake’

MW Magnitude

N Number of storey

Q Characteristic strength

Pcr Critical buckling load

PE Euler buckling load

PS Shear stiffness per unit length

R Seismic load reduction factor

S Shape factor

SD1 Design 5% damped spectral acceleration at 1 sec. Period

T Fixed-based period

TM Isolated period at maximum displacement

Teff Effective period

TD Isolated period at design displacement

TV Vertical fundamental period of vibration

tr Total thickness of rubber

to Thickness of single layer of rubber

WD Area of hysteresis loop

Wx Portion of W that is located at or assigned to level x

Wi Portion of W that is located at or assigned to level i

W Total weight of superstructure

VS Base shear force

� Damping ratio

�eff Effective viscous damping ratio

xx

�s Damping ratio of superstructure

�i Damping ratio of isolator

û+ Positive peak test displacements

û– Negative peak test displacements

�max Maximum shear strain

N Diameter

1

CHAPTER 1

INTRODUCTION

Seismic isolation, also known as base isolation in structures, is an innovative design

strategy that provides a practical alternate for the earthquake resistant design of new

structures and the seismic rehabilitation of existing buildings, bridges and industrial

establishments. The concept of seismic isolation is based on the premise that a

structure can be substantially decoupled from damaging horizontal components of

earthquake ground motions. Thus, earthquake induced forces may be reduced by

factors of five to ten from those that a conventional fixed-base structure would

experience.

During earthquake attacks, the traditional building structures in which the base is

fixed to the ground, respond with a gradual increase from ground level to the top of

the building, like an amplifier. This may result in heavy damage or total collapse of

structures. To avoid these results, while at the same time satisfying in-service

functional requirements, flexibility is introduced at the base of the structure, usually

by placing elastomeric isolators between the structure and its foundation. Additional

damping is also needed to control the relative displacement between the structure and

the ground.

2

1.1. Principles of Seismic Isolation

Seismic isolation is a design approach aimed at protecting structures against damage

from earthquakes by limiting the earthquake attack rather than resisting it. In

seismically base-isolated systems, the superstructure is decoupled from the ground

motion by introducing horizontally flexible but vertically very stiff components at

the base level of the structure. Thereby, the isolation system shifts the fundamental

time period of the structure to a large value and/or dissipates the energy in damping,

limiting the amount of force that can be transferred to the superstructure such that

interstory drift and floor accelerations are reduced drastically.

Typical earthquake accelerations have dominant periods of about 0.1-1.0 sec. with

maximum severity often in the range 0.2-0.6 sec. Structures whose natural periods of

vibration lie with in the range 0.1-1.0 sec. are therefore particularly vulnerable to

seismic attacks because they may resonate. The most important feature of seismic

isolation is that its increased flexibility increases the natural period of the structure

(>1.5 sec., usually 2.0-3.0 sec.). Because the period is increased beyond that of the

earthquake, resonance is avoided and the seismic acceleration response is reduced

[22]. The benefits of adding a horizontally compliant system at the foundation level

of a building can be seen in Figure 1.1.

Figure 1.1 Acceleration response spectrum [2]

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3 H U LR G

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3

In Figure 1.1, note the rapid decrease in the acceleration transmitted to the isolated

structure as the isolated period increases. This effect is equivalent to a rigid body

motion of the building above the isolation level. The displacement of the isolator is

controlled (to 100-400 mm) by the addition of an appropriate amount of damping

(usually 5-20 % of critical). The damping is usually hysteretic, provided by plastic

deformation of either steel shims or lead or ‘viscous’ damping of high-damping

rubber. For these isolators strain amplitudes, in shear, often exceed 100%. The high

damping has the effect of reducing the displacement by a factor of up to five from

unmanageable values of ~1.0 m to large but reasonable sizes of <300 mm [22]. High

damping may also reduce the cost of isolation since the displacements must be

accommodated by the isolator components and the seismic gap, and also by flexible

connections for external services such as water, sewage, gas and electricity.

The effect of damping for controlling displacement is shown in Figures 1.1 and 1.2,

with increased damping reducing both the displacement of, and the accelerations to,

the structure. But damping higher than 0.20 should be avoided since high isolator

damping may seriously distort mode shapes, and complicate the analysis. In addition,

higher mode responses increase as the damping increases. As a result of this

substantial contribution of higher modes, seismic inertia forces increase when

compared with those produced by only the first mode.

Figure 1.2 Displacement response spectrum [2]

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4

1.2 Seismic Isolation Systems

The successful seismic isolation of a particular structure is strongly dependent on the

appropriate choice of the isolator devices, or system, used to provide adequate

horizontal flexibility with at least minimal centering forces and appropriate damping.

It is also necessary to provide an adequate seismic gap that can accommodate all

intended isolator displacements.

Most systems used today incorporate either elastomeric bearings, with the elastomer

being either natural rubber or neoprene, or sliding bearings, with the sliding surface

being Teflon and stainless steel although other sliding surfaces have been used.

Systems that combine elastomeric bearings and sliding bearings have also been

proposed and implemented [3].

1.2.1 Elastomeric Bearings

These bearings are fully developed commercial products whose main application

have been for bridge superstructures, which often undergo substantial dimensional

and shape changes due to changes in temperature. More recently their use has been

extended to the seismic isolation of buildings and other structures. Elastomeric, non-

lead-rubber bearings are available as either low-damping natural rubber bearing or

high-damping bearings.

1.2.1.1 Low Damping Natural and Synthetic Rubber Bearings

Low-damping natural rubber bearings and synthetic rubber bearings are used in

conjunction with supplementary damping devices, such as viscous dampers, steel

bars, frictional devices, and so on. The elastomer used in bearings may be natural

rubber or neoprene. The isolators have two thick steel endplates and many thin steel

5

shims. The rubber bearing consists of layer of rubber 5-20 mm thick, vulcanized

between steel shims. The rubber layers give the bearing it’s relatively low shear

stiffness in the horizontal plane while the steel plates control the vertical stiffness and

also determine the maximum vertical load, which can be applied safely. The steel

plates also prevent the bulging of the rubber [1].

The material behavior in shear is quite linear up to shear strains above 100%, with

the damping range of 2-3% of critical. The material is not subject to creep, and long-

term stability of the modulus is good [5].

Low-damping elastomeric laminated bearings are simple to manufacture (the

compounding and bonding processes to steel is well understood), easy to model, and

their mechanical response is unaffected by rate, temperature, history, or aging.

However in the structures they must be used with supplementary damping systems.

These supplementary systems require elaborate connections and, in the case of

metallic dampers, are prone to low-cycle fatigue [1].

1.2.1.2 High Damping Natural Rubber Bearings

The energy dissipation in high-damping rubber bearings is achieved by special

compounding of the elastomer. Damping ratios will generally range between 8% and

20% of critical. The shear modulus of high-damping elastomers generally ranges

between 0.34 MPa and 1.40 MPa. The material is nonlinear at shear strains less than

20% and characterized by higher stiffness and damping, which minimizes the

response under wind load and low-level seismic load. Over the range of 20-120%

shear strain, the modulus is low and constant. At large shear strains, the modulus and

energy dissipation increase. This increase in stiffness and damping at large strains

can be exploited to produce a system that is stiff for small input, is fairly linear and

flexible at design level input, and can limit displacements under unanticipated input

levels that exceed design levels [1].

6

Figure 1.3 High damping rubber bearing [25]

1.2.1.3 Lead-Plug Bearings

Lead-plug bearings are generally constructed with low-damping elastomers and lead

cores with diameters ranging 15% to 33% of the bonded diameter of the bearing.

Laminated-rubber bearings are able to supply the required displacements for seismic

isolation [1]. By combining them with a lead-plug insert which provides hysteretic

energy dissipation, the damping required for a successful seismic isolation system

can be incorporated in a single compact component. Thus one device is able to

support the structure vertically, to provide the horizontal flexibility together with the

restoring force, and to provide the required hysteretic damping.

The maximum shear strain range for lead-plug bearings varies as a function of

manufacturer but is generally between 125% and 200%.

7

Figure 1.4 Lead-Plug bearing [25]

1.2.2 Isolation Systems Based on Sliding

One of the most popular and effective techniques for seismic isolation is through the

use of sliding isolation devices. The sliding systems perform very well under a

variety of severe earthquake loading and are very effective in reducing the large

levels of the superstructure's acceleration. These isolators are characterized by

insensitivity to the frequency content of earthquake excitation. This is due to

tendency of sliding system to reduce and spread the earthquake energy over a wide

range of frequencies. The sliding isolation systems have found application in both

buildings and bridges. The advantages of sliding isolation systems as compared to

conventional rubber bearings are:

(i) Frictional base isolation system is effective for a wide range of frequency

input,

(ii) Since the frictional force is developed at the base, it is proportional to the

mass of the structure and the center of mass and center of resistance of the

8

sliding support coincides. Consequently, the torsional effects produced by

the asymmetric building are diminished.

1.2.2.1 Pure-Friction System

The simplest sliding isolation system is the pure friction system. In this system a

sliding joint separates the superstructure and the substructure. The use of layer of

sand or roller in the foundation of the building is the example of pure-friction base

isolator. The pure-friction type base isolator is essentially based on the mechanism of

sliding friction. The horizontal frictional force offers resistance to motion and

dissipates energy. Under normal conditions of ambient vibrations and small

magnitude earthquakes, the system acts like a fixed base system due to the static

frictional force. For large earthquake the static value of frictional force is overcome

and sliding occurs thereby reducing the accelerations.

1.2.2.2 Resilient-Friction Base Isolation System

Mostaghel and Khodaverdian (1987) proposed the resilient-friction base isolation (R-

FBI) system as shown in Figure 1.5. This base isolator consists of concentric layers

of Teflon-coated plates that are in friction contact with each other and contains a

central core of rubber. It combines the beneficial effect of friction damping with that

of resiliency of rubber. The rubber core distributes the sliding displacement and

velocity along the height of the R-FBI bearing. They do not carry any vertical loads

and are vulcanized to the sliding ring. The system provides isolation through the

parallel action of friction, damping and restoring force [1].

9

Figure 1.5 Resilient-friction base isolation system [25]

1.2.2.3 Electric de France System

An important friction type base isolator is a system developed under the auspices of

“Electric de France” (EDF) (Gueraud et. al., 1985). This system is standardized for

nuclear power plants in region of high seismicity. The base raft of the power plant is

supported by the isolators that are in turn supported by a foundation raft built directly

on the ground. The main isolator of the EDF consists of laminated (steel reinforced)

neoprene pad topped by lead-bronze plate that is in friction contact with steel plate

anchored to the base raft of the structure. The friction surfaces are designed to have a

coefficient of friction of 0.2 during the service life of the base isolation system.

The EDF base isolator essentially uses elastomeric bearing and friction plate in

series. An attractive feature of EDF isolator is that for lower amplitude ground

excitation the lateral flexibility of neoprene pad provides base isolation and at high

level of excitation sliding will occur which provides additional protection. This dual

isolation technique was intended for small earthquakes where the deformations are

concentrated only in the bearings. However, for larger earthquakes the bronze and

steel plates are used to slide and dissipate seismic energy. The slip plates have been

designed with a friction coefficient equal to 0.2 and to maintain this for the life time

of the plant [1].

10

1.2.2.4 Friction Pendulum System

The concept of sliding bearings is also combined with the concept of a pendulum

type response, obtaining a conceptually interesting seismic isolation system known

as a friction pendulum system (FPS) (Zayas et al., 1990) as shown in Figure 1.6. In

FPS, the isolation is achieved by means of an articulated slider on spherical, concave

chrome surface. The slider is faced with a bearing material which when in contact

with the polished chrome surface, results in a maximum sliding friction coefficient of

the order of 0.1 or less at high velocity of sliding and a minimum friction coefficient

of the order of 0.05 or less for very low velocities of sliding. The dependency of

coefficient of friction on velocity is a characteristic of Teflon-type materials (Mokha

et al., 1990). The system acts like a fuse that is activated only when the earthquake

forces overcome the static value of friction. Once set in motion, the bearing develops

a lateral force equal to the combination of the mobilised frictional force and the

restoring force that develops as a result of the induced rising of the structure along

the spherical surface. If the friction is neglected, the equation of motion of the system

is similar to the equation of motion of a pendulum, with equal mass and length equal

to the radius of curvature of the spherical surface. The seismic isolation is achieved

by shifting the natural period of the structure. The natural period is controlled by

selection of the radius of curvature of the concave surface. The enclosing cylinder of

the isolator provides a lateral displacement restraint and protects the interior

components from environmental contamination. The displacement restraint provided

by the cylinder provides a safety measure in case of lateral forces exceeding the

design values [1].

11

Figure 1.6 Friction pendulum system [25]

1.3 Current Applications

The seismically isolated buildings fall into two broad categories: fragile structures of

historic significance and new structures with contents, which need to be protected or

continue to operate during and immediately after the earthquake. It is seen that most

base isolated buildings around the world are important buildings such as hospitals,

universities, schools, firehouses, nuclear power plants, municipal and governmental

buildings, and some high technology buildings that house sensitive internal

equipment or machinery.

There are many examples of base-isolated structures in the United States and Japan.

A number of base-isolated buildings have been built in New Zealand and in Italy.

Demonstration projects that apply low-cost base isolation systems for public housing

12

in developing countries have been completed in Chile, the People’s Republic of

China, Indonesia, and Armenia [4].

In the United States the most commonly used isolation system is the lead-plug rubber

bearing. Although some projects are isolated solely with lead-plug bearings, they are

generally used in combination with multilayered elastomeric bearings without lead

plugs.

Many isolation systems used in Japan and New Zealand combine low-damping

natural rubber bearings with some form of mechanical damper. This includes

hydraulic dampers, steel bars, steel coils, or lead plugs within the building itself.

There are several drawbacks to using dampers for isolating structures: Every type of

damper –except the internal lead plug- requires mechanical connectors and routine

maintenance, the yielding of metallic dampers introduces a nonlinearity into the

response that complicates the analysis of the dynamic response of the isolated

building, and they reduce the degree of isolation by causing response in higher

modes [2].

In Turkey, especially in some of the prestigious projects the application of seismic

isolation technique has started to be used in recent years. For example, the new $300

million International Terminal at Istanbul's Atatürk Airport is a massive, two

hundred and fifty thousand square meters building that serves as the port of entry for

14 million international air passengers to Turkey each year. The main feature of the

terminal is the 250m by 225m pyramidal roof space frame with triangular skylights.

This delicate roof structure is supported by 130 Friction Pendulum bearings, placed

between the roof frame and the concrete columns that rise 7m above the departure

level. The bearings protect the delicate roof glass, glass curtain walls, and the

cantilever columns in the event of a major earthquake. Some of the important

isolated buildings are listed in Table 1.1.

13

Table 1.1 Current applications of seismic isolation [4]

No Buildings Year City Size Description

1

Foothill Law and Justice Center, San

Bernardino 1985

Los Angeles,

USA

15800 m2 N = 4

21 km distance to the fault, 98 bearings, $38 million high

damping natural rubber.

2

Fire Command and

Control Facility 1997

Los Angeles,

USA

5000 m2 N = 2

High damping natural rubber 6% less cost than conventional

design.

3 Emergency

Operations Center 1998

Los Angeles,

USA

8000 m2 N = 3

28 high damping natural rubber bearings

4

Traffic Management

Center for Caltrans, Kearny

Mesa

1997 San Diego,

USA N = 2

40 bearings t= 60 cm TD = 2,5 sec., dD= 25 cm

5

M.L. King / C.R. Drew

Diagnostics Trauma Center

1995

Willowbrook Los

Angeles, USA

13000 m2 N = 5

70 high damping rubber bearings, 12 sliding pad

D=100cm

6

Flight Simulator Manufacturing

Facility 1998

Salt Lake City, USA

10800 m2 N = 4

50 pads 46cm / 48 pads 38cm TD = 2,5 sec., dD= 23 cm

7 Auto Zone Office

Building 1997

Memphis, USA

23230 m2 N = 8

43 rubber isolators $27 million

8

International Terminal,

San Francisco Airport

1999 San

Francisco, USA

28000m2 Friction Pendulum Isolators

9 Hayward City

Hall, CA 1999

Hayward, USA

14000m2 Friction Pendulum Isolators

10

West Japan Postal Computer

Center, Sanda 1986

Sanda, Japan

47000 m2 N = 6

120 elastomeric pads, TD=3,9 sec.

11

Matsumura-Gumi Technical

Research Institute 1989 Japan

12000 m2 N = 8

High damping natural rubber bearings

12

Administration Center, National

Telephone Company

1998 Ancona,

Italy

5 buildings 12000 m2

N=7

High damping rubber bearings

14

No Buildings Year City Size Description

13

Residential Apartment Building, Squillace

1999 Calabria,

Italy 2600 m2

N = 4 High damping rubber

bearings

14

Administrative Building,

Ministry of Defense

2000 Ancona,

Italy 6800 m2

N = 4 High damping rubber

bearings

15

William Clayton Building,

Wellington 1981

New Zealand

- Lead-Rubber bearings

16 Union House,

Auckland 1988

New Zealand

13600 m2 N = 13

Lead-Rubber bearings

17

Central Police Station,

Wellington 1989

New Zealand

12400 m2 N = 10

Lead-extension dampers

18 National Museum,

Wellington 1997

New Zealand

22000 m2 N = 6

142 lead-rubber bearings 36 teflon pads

19

Printing Press Building,

Peton, Wellington 1990

New Zealand

16000 m2 N = 4

Lead-Rubber bearings

1.4 Literature Survey

The codes and guidelines for design of structures with seismic base isolation have

evolved from the design provisions that were developed in the 1980s by a

subcommittee of the Structural Engineers Association of Northern California

(SEAONC). In 1986 SEAONC published a simple regulation titled “Tentative

Seismic Isolation Design Requirements”, also known as the Yellow Book [1]. The

Yellow Book, mainly based on equivalent static design methods, implemented in the

various editions of the Uniform Building Code (UBC) [9], the most widely used code

for design of earthquake resistant buildings in the United States. The Yellow Book

modified and became the 1991 version of the UBC, “Earthquake Regulations for

Seismic-Isolated Structures”. The 1994 and 1997 versions of UBC are elaborated. As

Table 1.1 (continued)

15

the UBC-97 has evolved, International Building Code 2000 [11] (IBC2000) has

become extremely complex code based mainly on dynamic methods of design.

The seismic upgrade design of existing structures is influenced by the National

Earthquake Hazards Reduction Program (NEHRP) Guidelines for the Seismic

Rehabilitation of Buildings, FEMA-273 [17], and its commentary FEMA-356 [16],

which are published by the Federal Emergency Management Agency. The FEMA-

273 provisions are very similar to those of the IBC2000 with one basic exception:

FEMA-273 permits pushover method.

In addition to the design codes, various textbooks are available providing complete,

up to date coverage of seismic isolation concept.

In their exceptional textbook, Naeim and Kelly [1] present detailed information

about current seismic isolation components. [1] serves as a guide to understand

isolation concept, procedures involved in design of seismic isolated structures, and

complex code requirements. UBC-97 is used for numerical examples and evaluated

in details. Where appropriate, UBC-97 requirements are compared and contrast with

those of FEMA-273 and other important documents. Furthermore, an overview of

available computer programs for analysis of seismic isolated structures and using the

SAP2000 nonlinear program to model nonlinear isolation systems are presented.

The more advanced textbook on seismic isolation is the one of Skinner, Robinson

and McVerry [2]. It explores the theoretical concepts in more detail. [2] mainly

concentrates on the mathematical analysis of the seismic responses of isolated

structures, discussion of isolation systems and guidelines to provide initial isolator

parameter values for engineers wishing to incorporate seismic isolation into their

designs.

In [4], Tezcan and Cimilli suggest a complete formulation similar to that of UBC-

1997 for use in a possible future version of the Turkish seismic code for designing

structures with seismic base isolation. It is advocated that the formulation supplied in

16

the Turkish seismic code [8], for the calculation of the lateral earthquake loads, can

be adjusted for the design of base isolated structures.

Matsagar and Jangid [20], in their noteworthy paper, present a study about the

influence of isolator characteristic parameters on the response of multi-story base

isolated structures. The effects of the shape of isolator loop and superstructure

flexibility on the seismic response is investigated.

1.5 Aims and Scope

The aim of this study is to investigate the effects of seismic base isolation systems,

especially rubber bearings, on the response of structures. The study includes analysis

of the seismic responses of isolated structures, which is oriented to give a clear

understanding of the processes involved and discussion of various isolators.

The notes introduce the related chapters of FEMA and IBC2000 regulations for the

seismic isolated structures. These provisions and formulas, their similarities and

differences, are presented. Case studies illustrate their use in both static and dynamic

analyses. The static equivalent lateral force of analysis, response spectrum analysis

and time history analysis are carried out in case studies. Design procedures used for

base isolated systems are discussed and form the basis for preliminary design

procedures. Using a consistent set of design criteria, a commercial computer program

SAP2000 demonstrates the ease with which the design for isolated systems may be

executed.

No specific provisions are included in the Turkish seismic code (ABYYHY-98) [8]

for the earthquake resistant design of buildings with seismic base isolation. Therefore

the seismic base isolation provisions of the FEMA [17] and IBC2000 [11] have been

utilized in the design examples. Nevertheless, the discussion of the case study results

is done by considering the Turkish seismic code and some important conclusions for

use in possible future version of the Turkish seismic code are drawn.

17

CHAPTER 2

MATHEMATICAL MODELLING OF ISOLATORS

Seismic isolation bearings are generally characterized as either linear viscoelastic

components or bilinear components. In practice all isolation bearings can be modeled

by bilinear models where as high-damping rubber bearings are generally modeled as

linear elastic-viscous models. For more detail explanation, one may refer to [20].

2.1 Mechanical Characteristics of Elastomeric Isolators

The horizontal stiffness of a bearing is given by [1]:

r

Ht

GK

)( Α= (2.1)

where G is the shear modulus of the elastomer, A is the total cross-sectional area, and

tr is the total thickness of the rubber only. Another design characteristic of an isolator

is the vertical stiffness KV which is the dominant parameter controlling the vertical

frequency of an isolated structure. The vertical stiffness of a rubber bearing is given

by the formula [1]:

r

C

Vt

EK

)( Α= (2.2)

18

where Ec is the instantaneous compression modulus of the rubber-steel composite

under the specified level of vertical load.

2.1.1 Comparison of Compression Modulus

The compression modulus of a circular bearing (Ec) is defined by different formulas

in FEMA-356 [16] and Naeim and Kelly study [1].

1

2)

3

4

6

1( −+=

KGSEC [FEMA-356] (2.3)

1

2)

1

6

1( −+=

KGSEC [Naeim and Kelly] (2.4)

Ec : Compression Modulus

S : Shape Factor (5< S < 30)

K : Bulk Modulus (1000MPa < K < 2500 MPa)

G : Shear Modulus (0.5MPa < G < 2.5 MPa)

Figures 2.1 – 2.3 are prepared in order to demonstrate how the compression modulus

of a circular pad changes according to these two different formulas for given

intervals of shape factor (S), bulk modulus (K), and shear modulus (G).

Ec – S Relationship

To be able to evaluate the effect of shape factor (S) only, shear modulus (G) and bulk

modulus (K) are taken as constant, 1.0 MPa and 2000 MPa, respectively. By

examining Figure 2.1, it can be said that the two formulas give very close results up

to S = 12. Thus, they can be assumed as identical for 5 < S < 12 interval. On the

other hand, for the “S” vales greater than 12 the outcomes of the formulas show

19

considerable difference and this difference increases as the “S” value increases. The

formula given by Naeim and Kelly gives greater compression modulus values when

compared to the formula given in FEMA for 12 ��6������LQWHUYDO�

Ec – G Relationship

Shape factor (S) and bulk modulus (K) are taken as 15 and 2000 MPa respectively, in

order to demonstrate the effect of shear modulus (G) in Figure 2.2. It is obvious from

the figure that the calculated “Ec” values from the formulas show considerable

difference and this difference increases as the “G” value increases. The formula

given by Naeim and Kelly gives greater compression modulus values when

compared to the formula given in FEMA for 0.5 MPa < G < 2.5 MPa interval.

Ec – K Relationship

In Figure 2.3 shape factor (S) and shear modulus (G) are taken as 15 and 1.0 MPa

respectively, in order to demonstrate the effect of bulk modulus (K). It is obvious

from the figure that the formula given by Naeim and Kelly gives greater compression

modulus values when compared to the formula given in FEMA. The calculated “Ec”

values from the two formulas show a constant difference in the range of 100 MPa no

matter what the value of “K” is.

20

Figure 2.1 Ec – S relationship

Figure 2.2 Ec – G relationship

G= 1.0MPa K= 2000MPa

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30 35

Shape Factor (S)

Co

mp

res

sio

n M

od

ulu

s (

Ec

) (M

Pa

)

FEMA F.NAEIM

6 �����. ������03D

0

200

400

600

800

1000

1200

1400

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Shear Modulus (G) (MPa)

Co

mp

res

sio

n M

od

ulu

s (

Ec

) (M

Pa

)

FEMA F.NAEIM

21

Figure 2.3 Ec – K relationship

The comparison of Figures 2.1–2.3 shows that Naeim and Kelly gives higher

compression modulus compared to FEMA for the same pad. Consequently, bearings

are assumed to be stiffer in vertical direction when compared to FEMA.

2.2 Equivalent Linear Model of Isolators

The non-linear force-deformation characteristic of the isolator can be replaced by an

equivalent linear model through effective elastic stiffness and effective viscous

damping. The equivalent linear elastic stiffness for each cycle of loading is

calculated from experimentally obtained force-deformation curve of the isolator and

expressed mathematically as [11]:

)(

)(−+

−+

∆−∆

−=

FFkeff (2.5)

G = 1.0M Pa , S = 15

0

100

200

300

400

500

600

700

800

900

1000

0 500 1000 1500 2000 2500 3000

Bulk M odulus (K) (M Pa)

Co

mp

res

sio

n M

od

ulu

s (

Ec

) (M

P

FEM A F. N A E IM

22

where F+ and F

– are the positive and negative forces at test displacements

û+�DQG�û–,

respectively. Thus, the keff is the slope of the peak-to-peak values of the hysteresis

loop as shown in Figure 2.4.

Figure 2.4 Force displacement relationship of

equivalent linear model [20]

The effective viscous damping ratio of the isolator calculated for each cycle of

loading is expressed as [11]:

[ ]2

loop

)(

)2(

−+ ∆−∆

Ε=

eff

effkπ

β (2.6)

where Eloop is the energy dissipation per cycle of loading.

2.3 Bilinear Model of Isolators

Bilinear model can be used for all isolation systems used in practice. In fact only

bilinear hysteretic model can reflect the non-linear characteristics of the lead-plug

bearings and friction-pendulum systems that are commonly used isolation systems.

The non-linear force-deformation behavior of the isolation system is modeled

through the bilinear hysteresis loop based on the three parameters (i) elastic stiffness,

8adUW��8�

6[eb^SUW_W`f�����

�8����� �

�8����� �

]WXX

23

K1 (ii) post-yield stiffness, K2 (iii) characteristic strength, Q (Figure 2.5). The

characteristic strength, Q is related to the yield strength of the lead plug inserted in

the elastomeric bearing or friction coefficient of the sliding type isolation system

[20].

8adUW

66k

�66[eb^SUW_W`f

=$=#

C

Figure 2.5 Force displacement relationship of bilinear model [1]

At specified design displacement, D, the effective stiffness for a bilinear system is

expressed as [1]:

)Q

(2D

Kkeff += D>Dy (2.7)

where Dy is the yield displacement. In terms of the primary parameters [1]:

)(

Q

21 KKDy

−= (2.8)

The�HIIHFWLYH�GDPSLQJ��eff is expressed as [1]:

)2(

)(Q42

Dk

DD

eff

y

effπ

β−

= (2.9)

24

2.4 Comparison of Response for Bilinear and Equivalent Linear Model

To investigate and compare the differences in the seismic responses of buildings

isolated by bilinear and equivalent linear isolator models, a five-story symmetrical

building, introduced in Section 3.2.2, is chosen. Two different types of isolators,

lead-plug bearings (LPB) and friction pendulum system (FPS), are used for bilinear

modeling where as type of the isolator is not important for equivalent linear

modeling. The nonlinear time history method is used for the analyses by the help of a

commercial computer program SAP2000. The earthquake motions selected for the

study are S50W component of 1979 Imperial Valley earthquake (IMPERIAL), EW

component of 1999 Kocaeli earthquake (KOCAELI), HORIZ0 component of 1989

Loma Prieta earthquake (LOMA). The peak ground acceleration (PGA) of Imperial

Valley, Kocaeli and Loma Prieta earthquake motions are 0.46g, 0.23g and 0.63g,

respectively. The acceleration and displacement spectra of the ground motions for

2% damping are shown in Figures 2.6 and 2.7. The damping ratio is selected as 2%

for thH�VSHFWUD�EHFDXVH� WKH�GDPSLQJ�UDWLR�RI� WKH� VXSHUVWUXFWXUH���s, is taken as 0.02

for the analyses.

Figure 2.6 Acceleration spectra

The investigated response quantities are the top floor acceleration and bearing

displacement. These response quantities are important because floor accelerations

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7 8 9

Time Period (sec)

Sp

ectr

al A

ccele

rati

on

(g

)

/20$,03(5,$/.2&$(/ø

25

developed in the structure are proportional to the forces exerted as a result of an

earthquake ground motion. On the other hand, the bearing displacements are crucial

in the design of isolation systems.

Figure 2.7 Displacement spectra

The parameters for the bilinear model isolators are determined according to the

parameters of equivalent linear model which are depended on the selected target

period T� DQG� WKH� HIIHFWLYH� YLVFRXV� GDPSLQJ��eff�� ,Q� DGGLWLRQ� WR� WKH� 7� DQG��eff, the

design displacement, D, is also necessary for the determination of the parameters of

bilinear model. The design displacement, equal to the maximum isolator

displacement, is calculated as a result of the analysis of the structure isolated by the

equivalent linear model isolators having the parameters T DQG��eff. For the assumed

value of yield displacement, Dy, depending upon the selected type of bilinear

isolation system, the parameters of bilinear hysteresis loop is determined such that it

KDV�D�SHULRG�DV�HTXDO�WR�7�DQG�GDPSLQJ�UDWLR�DV��eff by using Equations 2.7, 2.8 and

2.9 given above.

The values of design displacement, D, used for such transformation are 49.6, 29.6

and 24.9 cm under Imperial Valley, Kocaeli and Loma Prieta ground motions

respectively, obtained from equivalent linear model analysis with T=2.1 sec.,

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6 7 8 9

Time Period (sec)

Sp

ectr

al D

isp

lacem

en

t (c

m)

.2&$(/øø03(5ø$/LOMA

26

keff ����N1�P�DQG��eff=0.15. When the design displacement values, D, of the three

earthquakes are compared:

D (imperial valley) > D (kocaeli) > D (loma prieta)

If the spectra given in Figures 2.6 and 2.7 are taken into account for T = 2.1 sec., this

is an expected trend. Because according to the acceleration spectra and displacement

spectra, while Imperial Valley earthquake gives the most critical results, Loma Prieta

earthquake gives the least critical values when T = 2.1 sec.

Table 2.1 The parameters of bilinear hysteresis loop

Imperial Valley Kocaeli Loma Prieta

D (cm) 49.6 29.6 24.9

Dy (mm) 2.5 (typical for FPS)

25 (typical for

LPB)

2.5 (typical for FPS)

25 (typical for

LPB)

2.5 (typical for FPS)

25 (typical for LPB)

Q (kN) 94.6 99.1 56.6 61.3 47.7 52.5

K2 (kN/m) 614.4 605.3 613.7 597.8 613.4 594.2

K1 (kN/m) 38438 4568 23253 3049 19689 2693

For the bilinear isolator models, two values of yield displacement, Dy, are taken into

account as 2.5 mm and 25 mm which mostly correspond to friction pendulum system

(FPS) and lead-plug bearing (LPB) isolators [1], respectively. The time variation of

top floor acceleration and bearing displacement is given in Figures 2.8 and 2.9 under

the effect of Imperial Valley earthquake for bilinear and linear isolator models. The

peak top floor accelerations obtained by bilinear hysteretic model are 0.59g and

0.43g for the yield displacement of 2.5mm and 25mm respectively. The

corresponding peak top floor acceleration obtained from equivalent linear model is

0.38g. This implies that the equivalent linear model as compared to bilinear

hysteretic model underestimates the force exerted on superstructure by the ground

motion.

27

On the other hand, the peak bearing displacement obtained by the bilinear hysteretic

model is 22.9 and 26.2 cm for the yield displacements of 2.5 and 25 mm,

respectively, whereas, that obtained from its equivalent linear model is 49.6 cm. This

implies that the equivalent linear model when compared to bilinear hysteretic model

overestimates the bearing displacement in an isolated structure. Similar results of

equivalent linear model and bilinear hysteretic model is also observed for Kocaeli

and Loma Prieta earthquake ground motions which are shown in Table 2.2.

Table 2.2 Results of the analyses

Maximum Top Floor Acceleration Maximum Bearing Displacement

Bilinear Bilinear

Ground Motion Linear

Typical FPS

Dy = 2.5 mm

Typical LPB

Dy = 25 mm

Linear Typical FPS

Dy = 2.5 mm

Typical

LPB

Dy = 25 mm

Imperial Valley 0.38g 0.59g 0.43g 49.6 cm 22.9 cm 26.2 cm

Kocaeli 0.11g 0.32g 0.21g 29.6cm 9.2cm 14.0cm

Loma Prieta 0.09g 0.25g 0.18g 24.9cm 6.9cm 8.6cm

As a result, it can be concluded that the equivalent linear model underestimates the

peak superstructure acceleration and overestimates the bearing displacement when

compared to the actual bilinear hysteretic model.

In Figures 2.9, 2.11 and 2.13 time variation of bearing displacements are given under

the effect of Imperial Valley Earthquake, Kocaeli Earthquake and Loma Prieta

Earthquake, respectively. It is observed from the figures that a permanent

displacement, which is a result of yielding in bearings, takes place for bilinear

models. This outcome shows the necessity of installing a supplementary system

producing re-centering force for the bearings.

In Figures 2.14, 2.15 and 2.16, force-deformation diagrams of bilinear models are

given in order to understand the effect of isolator yield displacement on the response

28

of an isolated structure. It is observed that the bearing displacements show an

increasing trend with the increase in the isolator yield displacement. For example; the

peak bearing displacements for Kocaeli earthquake read from the Figure 2.15 are 9.2

cm and 14.0 cm for the yield displacement of 2.5mm and 25mm respectively. Since

the same trend is also valid for the other ground motions, it can be concluded that

with the increase in isolator yield displacement, Dy, the bearing displacement also

increases. But the percentage of the increase depends on the effectiveness of the

source type.

29

Figure 2.8 Time variation of top floor acceleration under the effect of Imperial Valley (1979) earthquake.

����������������

�������������

� � �� �� �� �� �� �� ��

7LPH��VHF�

7RS�)

ORRU�$

FFHOHU

DWLRQ

��J� /,1($5

'\� �����PP'\� ����PP

30

Figure 2.9 Time variation of bearing displacement under the effect of Imperial Valley (1979) earthquake.

�������������

������������

� � �� �� �� �� �� �� ��

7LPH��VHF�

%HDUL

QJ�'L

VSODF

HPHQ

W��FP�

/,1($5'\� �����PP'\� ����PP

31

Figure 2.10 Time variation of top floor acceleration under the effect of Kocaeli (1999) earthquake.

����

��

����

�

���

�

���

� � �� �� �� �� �� �� ��

7LPH��VHF�

7RS�)

ORRU�$

FFHOHU

DWLRQ

��J�

),;('/,1($5'\� �����PP'\� ����PP

32

Figure 2.11 Time variation of bearing displacement under the effect of Kocaeli (1999) earthquake.

�������������

��������

� � �� �� �� �� �� �� ��

7LPH��VHF�

%HDUL

QJ�'L

VSODF

HPHQ

W��FP�

/,1($5

'\� �����PP

'\� ����PP

33

Figure 2.12 Time variation of top floor acceleration under the effect of Loma Prieta (1989) earthquake.

-3

-2

-1

0

1

2

3

0 5 10 15 20 25 30 35 40 45

T ime (se c)

To

p F

loo

r A

ccel

erat

ion

(g

)

FIXED

LINEA R

Dy =2,5

Dy =25

34

Figure 2.13 Time variation of bearing displacement under the effect of Loma Prieta (1989) earthquake.

���

���

���

�

��

��

��

� � �� �� �� �� �� �� �� ��

7LPH��VHF�

%HDUL

QJ�'L

VSODF

HPHQ

W��FP�

/,1($5'\� �����PP'\� ���PP

35

Figure 2.14 Force-deformation behavior for Imperial Valley Earthquake

(bilinear hysteretic models)

Figure 2.15 Force-deformation behavior for Kocaeli Earthquake

(bilinear hysteretic models)

��������

�������

���� ���� ���� � ��� ��� ���

%HDULQJ�'LVSODFHPHQW��P�,PSHULDO�9DOOH\������'\� �����PP

)��N1

�� �

��������

�������

���� ���� ���� � ��� ��� ���

%HDULQJ�'LVSODFHPHQW��P�,PSHULDO�9DOOH\�������'\� ���PP

)��N1

��

�

��������������

���� ���� ���� � ��� ��� ���

%HDULQJ�'LVSODFHPHQW��P�.RFDHOL�������'\� �����PP

)��N1

�� �

��������������

���� ���� ���� � ��� ��� ���

%HDULQJ�'LVSODFHPHQW��P�.RFDHOL�������'\� ����PP

)��N1

��

36

Figure 2.16 Force-deformation behavior for Loma Prieta Earthquake

(bilinear hysteretic models)

����

�������

���

���� ���� ���� � ��� ��� ���

%HDULQJ�'LVSODFHPHQW��P�/RPD�3ULHWD�������'\� ����PP

)��N1

�� �

����

����

���

���

���� ���� ���� � ��� ��� ���

%HDULQJ�'LVSODFHPHQW��P�/RPD�3ULHWD�������'\ ���PP

)��N1

�� �

37

CHAPTER 3

CASE STUDIES

3.1 Introduction

The aim of the case studies is to investigate the performance features and response

mechanisms of base isolated structures for different code specifications. Major

characteristics of seismic isolation systems are introduced and studied in the previous

chapters. Four different types of buildings are used in the analyses. The isolated

buildings are analyzed by using Static Equivalent Lateral Force, Response Spectrum

and Time History methods. A commercial computer package, namely SAP2000, is

used for 3D analysis of the structures. The analyses of these isolated buildings are

done for each soil type that is mentioned in the Turkish Seismic Code (Z1, Z2, Z3,

and Z4).

The basic motive in the studies is to identify the similarities and differences between

the design code IBC2000, and design specification FEMA 273, and make a

comparison between them from the design of base isolated structures point of view.

3.2 Description of the Structures

The structures, used for the analyses, are assumed to be serving as school buildings.

The detailed descriptions of the buildings are as follows:

38

3.2.1 Three-Storey Symmetrical Building (Type-I)

The three-storey building has a regular plan (36m x 12m) as shown in Figure 3.1.

The structural system is selected as concrete frames with identical columns of 50/50

centimeters in size, and beams of dimension 40/70 centimeters. Each floor slab has

15 centimeters thickness and the story height is 3 meters. The critical damping ratio

of superstructure is taken as 2% for isolated cases.

Figure 3.1 Plan view of symmetrical building types.

28 units High Damping Rubber bearings (HDR) are used for the isolation of the

building. The detailed calculations of isolation system design are explained in

Section 4.1. The bearings have the following linear properties accordingly:

�i = 0.15 (isolator damping ratio)

G = 500 kN/m2

Kh = 805 kN/m

Kv = 500000 kN/m

39

Figure 3.2 Section view of building Type-I

3.2.2 Five-Storey Symmetrical Building (Type-II)

The five-storey building has a regular plan (36m x 12m) as shown in Figure 3.1. The

structural system and seismic isolation system is identical with three-storey

symmetrical building.

Figure 3.3 Section view of building Type-II

40

3.2.3 Eight-Storey Symmetrical Building (Type-III)

The eight-storey building has a regular plan (36m x 12m) as shown in Figure 3.1.

The structural system and seismic isolation system is identical with three-storey

symmetrical building.

Figure 3.4 Section view of building Type-III

3.2.4 Non-symmetrical Building (Type-IV)

The plan view of five storey non-symmetrical building is shown in Figure 3.5 below.

The structural system is selected as concrete frames with identical columns of 50/50

centimeters in size, and beams of dimension 40/70 centimeters. Each floor slab has

15 centimeters thickness and the story height is 3 meters. The critical damping ratio

of superstructure is taken as 2% for isolated cases.

41

Figure 3.5 Plan view of building Type-IV.

Figure 3.6 Section views of building Type-IV.

22 units High Damping Rubber bearings (HDR) are used for the seismic isolation of

the building. The linear properties of the selected isolators are as follows:

�i = 0.15 (isolator damping ratio)

G = 500 kN/m2

Kh = 805 kN/m

Kv = 500000 kN/m

42

3.3 Analysis Methods

In this section, static equivalent lateral force procedure, response spectrum analysis

and time history analysis are discussed.

3.3.1 Static Equivalent Lateral Force Procedure

The isolation system should be designed to withstand minimum lateral earthquake

displacements, DD, that act in the direction of each of the main horizontal axes of the

structure in accordance with the following [24]:

D

DD

DB

TSgD 1

2)

4(

π= (3.1)

where:

BD = Numerical coefficient related to the effective damping of the

isolation system at design displacement, as set forth in Table 3.1

g = Acceleration of gravity

SD1 = Design 5% damped spectral acceleration at 1 sec. period

TD = Isolated period at design displacement

Table 3.1 Damping coefficient [11]

EFFECTIVE DAMPING

��i) BD

<2% 0.8

5% 1.0

10% 1.2

20% 1.5

30% 1.7

40% 1.9

>50% 2.0

43

For damping values other than the one specified in Table 3.1, linear interpolation can

be done to find corresponding BD value. Alternatively, a very close approximation to

the table values is given by;

)ln1(25.01

β−=DB

(3.2)

The effective period of the isolated structure, TD, is determined as:

gK

WT

h

D π2= (3.3)

where W is the total dead load weight of the superstructure.

“The total design displacement, DTD, of elements of the isolation system shall

include additional displacement due to actual and accidental torsion calculated

considering the spatial distribution of the lateral stiffness of the isolation system and

the most disadvantageous location of mass eccentricity. DTD must satisfy the

following condition.” [11]:

++≥

22

121

db

eyDD DTD (3.4)

where:

d = Shortest plan dimension

b = Longest plan dimension

e = The actual eccentricity measured in plan between the center of mass

of the structure and the center of stiffness of the isolation system,

plus the accidental eccentricity taken as 5% of the longest plan

dimension of the structure perpendicular to the direction of seismic

loading under consideration (Figure 3.7).

44

Figure 3.7 Plan dimensions for calculation of DTD [1].

The structure above the isolation system must be designed to withstand a minimum

total shear force, VS:

R

DKV Dh

S = (3.5)

where:

R = Seismic load reduction factor.

While FEMA 273 assumes R as equal to one for isolated structures (the structure

deforms only in elastic range), IBC2000 takes it as if the structure goes into inelastic

range (1.0�5������� ,Q� WKLV� VWXG\� 5� LV� DVVXPHG� EH� HTXDO� WR� RQH� IRU� ERWK� RI� WKH�specifications, thus the lateral EQ force, applied to the building is not reduced. One

can easily calculate the corresponding design values of R=2.0 if it is desired.

The total shear force, VS, is distributed over the height of the structure as given by:

∑=

=n

i

ii

xxS

x

hW

hWVF

1

(3.6)

45

where:

hi = Height above the base to level i.

hx = Height above the base to level x.

Wx = Portion of total dead load that is located at or assigned to level x.

Wi = Portion of total dead load that is located at or assigned to level i.

3.3.2 Response Spectrum Analysis

The 5% damped spectrum, given in Turkish seismic code (ABYYHY-98, [8]), is

used for the analysis of building and the spectrum is modified for each of the soil

types (Z1, Z2, Z3, Z4). Spectrum is assumed to be acting on the building from both

directions (X-Y) simultaneously. While the component applied from one axis is

multiplied by 1.00; the orthogonal component is multiplied by 0.30. According to

this logic, two different E.Q. combinations are applied to the structure and the results

are examined for each case. In the results, the one, which causes the most critical

condition, is taken into account.

Figure 3.8 Response spectrum functions given in Turkish Seismic Code.

Re s pons e Spe ctrum

0

0 .5

1

1 .5

2

2 .5

3

0 0 .5 1 1 .5 2 2 .5 3 3 .5 4 4 .5T (s )

Acc

eler

atio

n (m

/s2

)

46

3.3.3 Time History Analysis

“Time history analysis shall be performed with at least three appropriate pairs of

horizontal time history components. If three time history analyses are performed, the

maximum response of the parameter of interest shall be used for design. If seven or

more time history analyses are performed, the average value of the response

parameter of interest shall be used for design. Each pair of histories shall be applied

simultaneously to the model.” [11]

The used ground motions and their properties are given in Table 3.2 below:

Table 3.2 Ground motions used in time history analyses

Düzce

Earthquake

Marmara

Earthquake

Coyote

Lake

Earthquake

Superstitn

Hills

Earthquake

Imperial

Valley

Earthquake

Landers

Earthquake

Loma

Prieta

Earthquake

Place Düzce,

Turkey

Kocaeli,

Turkey

Coyote

Lake,

U.S.A.

Superstitn

Hills,

U.S.A.

Imperial

County,

U.S.A.

Yucca

Valley,

U.S.A.

Santa Cruz

County,

U.S.A.

Date 12.11.1999 17.08.1999 06.08.1979 24.11.1987 15.10.1979 28.06.1992 17.10.1989

Magnitude

(MW) 7.2 7.4 5.7 6.7 6.6 7.4 7.1

Closest

Distance to

Fault Rupture

(km)

8.23 3.28 3.20 4.30 27.03 9.00 18.00

Number of

Data Points 5180 7001 5764 2221 1845 4000 2000

Time Interval

(sec.) 0.005 0.005 0.005 0.01 0.02 0.02 0.02

3.4 Design Codes

Since there are no provisions available in the Turkish seismic code for design of base

isolated structures; in this study the design procedure for isolated buildings is

primarily based on International Building Code 2000 (IBC2000) [11] and Federal

Emergency Management Agency (FEMA 273) [17] provisions.

47

The applicable methods in IBC2000 and FEMA 273 for the design of an isolated

building and necessary formulas of these methods are mentioned above. In addition,

some important limiting regulations in the design procedure are also stated in the

IBC2000 and FEMA 273.

In both IBC2000 and FEMA 273, it is stated that the conditions of site where the

structure is located must be reflected into the design procedure. Consequently, the

calculated response of the structure is modified. A coefficient called as scaling factor

is involved in design calculations for this purpose. In the following paragraphs,

scaling concept was given for both of the codes.

3.4.1 IBC2000

The base shear, VS, is taken as not less than the following threshold values for static

equivalent lateral force procedure:

��The lateral seismic force required for a fixed-base structure of the same

weight and a period equal to the isolated period.

��The base shear corresponding to the factored design wind load.

��The lateral seismic load required to exceed the isolation system (the yield

level of a softening system, the break away friction level of a sliding system

factored by 1.5).

When the factored base shear force on structural elements, determined using either

response spectrum or time history analysis, is less than the minimum prescribed

below, response parameters, including member forces and moments, is adjusted

proportionally upward.

��The total design displacement of isolation system is taken as not less than

90% of DTD as specified in Equation 3.4.

48

��The design base shear force on the structure above the isolation system, if

regular in configuration, is taken as not less than 80% of VS as prescribed by

Equation 3.5.

In IBC2000 there are two exceptions for the above conditions:

1. The design base shear force on the structure above the isolation

system, if regular in configuration, is permitted to be taken as less

than 80%, but not less than 60% of VS, provided time history analysis

is used for design of the structure. The design base shear force on the

structure above the isolation system, if irregular in configuration, must

be taken as not less than VS.

2. The design base shear force on the structure above the isolation

system, if irregular in configuration, is permitted to be taken as less

than 100%, but not less than 80% of VS, provided time history

analysis is used for design of the structure.

The scaling limits on displacements specified above must be evaluated using values

of DTD determined in accordance with Equation 3.4 except that DD’ is permitted to be

used instead of DD where DD’ is prescribed by the following formula:

DD’ =2

)(1D

D

T

T

D

+ (3.7)

where:

T = Elastic, fixed-based period of the structure above the isolation

system.

TD = Effective period, in seconds, of the seismically isolated structure at

the design displacement in the direction under consideration as

prescribed by Equation 3.3.

49

Table 3.3 Scaling limits for IBC2000

If Response Spectrum is Used If Time History Analysis is Used

Vs ������9s ������9s Regular

DTD ������'TD’ ������'TD’

Vs ������9s ������9s Irregular

DTD ������'TD’ ������'TD’

3.4.2 FEMA 273

The value of VS is taken as not less than the following for static equivalent lateral

force procedure:

��The base shear corresponding to the factored design wind load.

��The lateral seismic load required to fully activate the isolation system

factored by 1.5 (include the yield level of a softening system, the break away

friction level of a sliding system).

If the total design displacement determined by response spectrum analysis is found to

be less than the value of DTD prescribed by Equation 3.4, then all response

parameters, including component actions and deformations, must be adjusted upward

proportionally to the DTD value and used for design.

If the design displacement determined by time history analysis is less than the value

of DD’ prescribed by Equation 3.7, then all response parameters, including

component actions and deformations, must be adjusted upward proportionally to the

DD’ value and used for design.

50

CHAPTER 4

ISOLATION SYSTEM DESIGN

4.1 Design of High Damping Rubber Bearing

As an example of isolation system design, the symmetrical building, introduced in

Section 3.2.2, is considered. The designed HDR bearings are used also for the other

building types analyzed in the case studies.

Twenty-eight HDR bearings are used for the isolation of the building. The selected

strategy for the design is to use one type of bearing for the whole system. The basic

structural data to be used for the design is as follows:

TD = 2.00 sec. (Target period for ‘Design Level’ earthquake)

TM = 2.50 sec. (Target period for ‘Max. Capable Level’ earthquake)

R = 1.00 (Seismic load reduction factor)

G = 500 kN/m2 (For large shear strains)

G = 700 kN/m2 (For small shear strains)

K = 2,000,000 kN/m2 (Bulk modulus)

�i = 15% (Damping ratio of isolator)

WT = 22330 kN (Total weight of the structure)

�max = 150%

The site is assumed to be located in seismic zone 1 with Z1 soil type.

51

In [1], it is stated that: “Seismic faults are grouped into three categories based on the

seriousness of the hazard they represent. Faults capable of producing large

magnitude earthquakes (M>7.0) and have a high rate of seismic activity (annual

average seismic slip rate, SR, of 5 mm or more) are classified as type A sources.

Faults capable of producing moderate magnitude earthquakes (M<6.5) with a

relatively low rate of seismic activity (SR<2 mm) are classified as type C sources.

All faults other than types A and C are classified as type B sources”.

The distance of the site to the nearest active fault is assumed to be less than 2 km;

and the fault type is assumed to be type A. As a result of these conditions SD1 is

equal to 0.64.

4.1.1 Lateral Stiffness of Base Isolators

By using Equation 3.3 for ‘Design Level Earthquake’:

81.9

22330200.2

totalkπ= : ktotal = 22465.7 kN/m

35.80228

7.22465==Dk kN/m (for one bearing)

For ‘Maximum Capable Earthquake Level’:

81.9

22330250.2

totalkπ= : ktotal = 14378 kN/m

50.51328

14378==Mk kN/m (for one bearing)

52

where kD and kM are the minimum lateral stiffness of base isolation bearings

corresponding to the ‘design earthquake’ and ‘maximum capable earthquake’,

respectively.

4.1.2 Estimation of Lateral Displacements

From Equation 3.1

23.038.1

00.264.0)

4

81.9(

2=

×=

πDD m

29.038.1

50.264.0)

4

81.9(

2=

×=

πMD m

where DD and DM are the displacements of the isolation system corresponding to the

‘design earthquake’ and ‘max. capable earthquake’, respectively. The damping

reduction factor B=1.38 is obtained from Equation 3.2.

4.1.3 Estimation of Disc Dimensions

Thickness of the disc can be calculated by,

maxγ

D

r

Dt = (4.1)

Therefore

153.05.1

23.0==rt m

Take

tr = 20 cm

53

'LVF�GLDPHWHU��N��LV�HVWLPDWHG�E\�XVLQJ�(TXDWLRQ�����

321.0500

2.035.802=

×=A m

2

N� �������P

Take

N� ����FP A = 0.322 m2

4.1.4 Actual Bearing Stiffness & Revised Fundamental Period

8052.0

500322.0=

×=Dk kN/m

2254080528 =×=totalk kN/m

997.181.922540

223302 =

×= π

DT sec.

It is seen that the calculated revised value of TD = 1.997 sec. is very close to the

target period of T = 2.00 sec.

4.1.5 Bearing Detail

For compressive stresses under vertical loads, the isolators undergo relatively smaller

VKHDU� VWUDLQV� RQ� WKH� RUGHU� RI� �� � ������ 7KHUHIRUH�*� � ���� N1�P2 should be used.

Shape factor, S, is selected as 8. The compression modulus, Ec, from Equation 2.4 is:

54

45.953,236200000087006

2000000870062

2

=+××

×××=CE kN/m

2

where the total vertical stiffness is determined from Equation 2.2 as,

5.861,681,1020.0

45.23695328322.0=

××=Vk kN/m

The vertical displacement, ¨Wv, becomes;

3

1009.25.10681861

22330 −×===∆V

vk

Wt m

The vertical fundamental period of vibration is given by;

S

TT H

V6

= (4.2)

gives,

102.086

00.2=

×=

VT sec.

As a result S = 8 is adequate.

ot

S4

Φ= (4.3)

where to is the thickness of single layer of rubber.

2084

640=

×=ot mm

200=× otn mm 10=n layers

55

Consequently, the design of the bearing is completed as shown in Figure 4.1. The

end plates are 25mm thick, and the steel shims are 2mm each. The total height is:

268)29()2010()252( =×+×+×=h mm

7KH�VWHHO�VKLPV�ZLOO�KDYH�D�GLDPHWHU�Ns = 630 mm, giving 5mm cover.

Figure 4.1 Detail design of isolator.

4.1.6 Buckling Load

EScr PPP = (4.4)

GAPS = (4.5)

2

2 )(

r

eff

Et

EIP

π= (4.6)

IEEI Ceff3

1)( = (4.7)

56

: 50832.03

25.032.045.236953500322.02

42

=×

××××××=

ππcrP kN

Maximum vertical load for one isolator is calculated from tributary area:

5.1085223301236

5.36)( max =×

×

×=VF kN

Factor of Safety, 68.45.1085

5083==FS

4.2 Performance Comparison of Isolation Systems

The design of a seismic isolation system involves many interrelated variables such as

targeted period of the isolated structure, base shear and damping of isolation system.

To illustrate an overview of how these variables affect the structural design, the

IBC2000 requirements for isolated buildings is used.

In the code, the displacement across the isolators (DD), the isolation period (TD) and

the base shear (VS) are given by Equations 3.1, 3.3, and 3.5. It is clear from

Equations 3.1 and 3.5 that the damping provided by the isolation system reduces both

the base shear and isolator displacement.

In order to compare the impact of the variables, involved in design procedure, on the

performance of isolation systems with different damping values; a basis must be

established. There are three alternatives cases;

¾�The seismic isolation systems have the same base shear.

¾�The seismic isolation systems have the same displacement.

¾�The seismic isolation systems have the same isolated period.

57

Each of these alternatives is evaluated with regard to their overall impact. In order to

be able to easily follow, numerical comparison of a 10% damped (BD = 1.2), a 15%

damped (BD = 1.35), and a 20% damped (BD = 1.5) systems is discussed. 10%, 15%,

and 20% damping values are selected for the comparison since they are in the

practical range of currently available systems.

Equal Base Shear

When the base shear of two isolated systems is equal, the relationships for isolation

period and displacement can be derived from Equations 3.1, 3.3 and 3.5.

V1 = V2

r

TT 2

1 =

2

21

r

DD =

where 2

1

B

Br =

B1 and B2 are the damping factors for the two isolation systems. To state these

relations numerically:

V10 = V20 V15 = V20

T10 = 1.25 T20 T15 = 1.11 T20

D10 = 1.56 D20 D15 = 1.24 D20

From Figure 4.2 it is seen that for an equal base shear, 10% and 15% damped

systems will require 25% and 11% longer periods and will produce 1.56 and 1.24

times the displacements of a 20% damped system.

58

Figure 4.2 Effect of damping for equal base shear case.

Equal Isolated Periods

When the isolated period of two systems is equal, the relationships for base shear and

displacement can be derived from Equations 3.1, 3.3 and 3.5.

T1 = T2

r

VV 2

1 =

r

DD 2

1 =

To state these relations numerically:

T10 = T20 T15 = T20

V10 = 1.25 V20 V15 = 1.11 V20

D10 = 1.25 D20 D15 = 1.11 D20

H!H

F!F

$"

$"

F!F$"

6!6$"

#"��6S_bWV#'��6S_bWV$"��6S_bWV

#"��6S_bWV

#'��6S_bWV

$"��6S_bWV

# ""

# "" # ## # $'

# "" # ## # $'

# '(# $&# ""

59

H!H

F!F

$"

$"

F!F$"

6!6$"

#"��6S_bWV#'��6S_bWV$"��6S_bWV

#"��6S_bWV

#'��6S_bWV

$"��6S_bWV

# ""

# ""

# $'# ### ""

# $'# ### ""

Figure 4.3 Effect of damping for equal period case.

For an equal isolated period, while 10% damped system will produce 25% greater

displacement and base shear, 15% damped system will produce 11% greater

displacement and base shear when compared to 20% damped system.

Equal Displacements

When the displacements of two isolated systems are equal, the relationships for

isolation period and base shear can be derived from Equations 3.1, 3.3 and 3.5.

D1 = D2

21 .TrT =

2

21

r

VV =

60

To state these relations numerically:

D10 = D20 D15 = D20

T10 = 0.8 T20 T15 = 0.9 T20

V10 = 1.56 V20 V15 = 1.24 V20

Thus, for an equal displacement, 10% and 15% damped systems will require 20%

and 10% lower periods and will produce 1.56 and 1.24 times the base shear of a 20%

damped system.

Figure 4.4 Effect of damping for equal displacement case.

H!H

F!F

$"

$"

F!F$"

6!6$"

#"��6S_bWV#'��6S_bWV$"��6S_bWV

#"��6S_bWV#'��6S_bWV$"��6S_bWV

# ""

" *" " +" # ""

" *" " +" # ""

# ""

# $&

# '(

61

CHAPTER 5

ANALYSIS & DISCUSSION OF RESULTS

5.1 Analysis of the Base Isolated Symmetrical Building

In this section “scaling” phenomenon mentioned in FEMA-273 & IBC2000 and the

differences between these two codes from the “scaling” point of view are discussed

for the symmetric buildings. To facilitate a study of the code provisions, building

Types I, II and III are selected. The description of the buildings is introduced in

Section 3.2. The high damping rubber bearings, HDR, designed in Section 4.1 are

used for the isolation of the all buildings. Response spectrum analysis, described in

Section 3.3.2, is carried out on building Types I, II and III. In addition, static

equivalent lateral force and time history analyses, described in Section 3.3.1 and

3.3.3, are performed for Type II which typifies the class of symmetrical structure that

is encountered in design. The analyses of the isolated buildings are done for each soil

type that is given in the Turkish Seismic Code (Z1, Z2, Z3, and Z4).

5.1.1 Scaling of the Results

The results of the analyses are scaled according to both FEMA-273 and IBC2000 as

mentioned in Section 3.4. The detailed calculation of scaling factors for each analysis

method is given below.

62

5.1.1.1 Scaling for Static Equivalent Lateral Force Procedure

The limits of scaling mentioned in FEMA-273 and IBC2000 for static equivalent

lateral force procedure are the same except that an additional limit is defined in

IBC2000: “The base shear must be greater than the lateral seismic force required for

a fixed-base structure of the same weight and a period equal to the isolated period”.

Building Type-II is analyzed with static equivalent lateral force procedure and the

results of the analysis are scaled according to the mentioned limit. For the calculation

of the lateral seismic force, VT, the procedure described in Turkish Seismic Code is

used.

T

T

T WITR

TAWV ××>

×= 10.0

)(

)(

1

1 (5.1)

)()( 101 TSIATA ××= (5.2)

A0 = 0.40

I = 1.4

R = 8 (Seismic load reduction factor for non-isolated building)

WT = 22330 kN

TD = 2.09 sec.

Table 5.1 Calculation of scaling factor for Type-II according to IBC2000

S(T) A(T)

(Equation 5.2)

VT (kN)

(Equation 5.1)

VS (kN)

(Equation 3.5) Scaling Factor

Z1 0.529 0.296 826 5432 no need to scale

Z2 0.666 0.373 1041 6790 no need to scale

Z3 0.921 0.516 1440 9670 no need to scale

Z4 1.274 0.713 1990 11027 no need to scale

63

5.1.1.2 Scaling for Response Spectrum Analysis

Building Types I, II and III are analyzed with response spectrum analysis and the

results of the analysis are scaled according to both FEMA-273 and IBC2000. To be

comprehendible, the parameters needed for the calculation of scaling factors are

given below. The damping coefficient, BD, is taken as 1.38 for the calculations since

the HDR, bearings designed in Section 4.1, are used for the isolation. As a result of

the modal analysis the fixed based period T, and isolated period TD of the buildings

are determined as:

Table 5.2 Fixed and isolated periods of buildings

Type-I Type-II Type-III

T (sec.) 0.27 0.45 1.57

TD (sec.) 1.57 2.09 2.73

Scaling according to IBC2000:

When IBC2000 is considered, the design displacement determined by response

spectrum analysis, Danalysis, must be greater than 90% of DTD' as specified in Equation

3.4. On the other hand, the design base shear force on the structure above the

isolation system must be greater than 80% of VS as prescribed by Equation 3.5.

Otherwise, all response parameters, including inertial forces and deformations, must

be adjusted proportionally upward.

When the results of the analyses are examined, it is seen that the first scaling limit,

Danalysis > 0.9×DTD', is more critical than the second one and results in greater scaling

factors. Therefore, displacement dependent scaling limit is used in the scaling factor

calculations.

64

Table 5.3 Calculation of scaling factor for Type-I according to IBC2000

SD1 DD (cm)

(Equation 3.1)

DD' (cm)

(Equation 3.7)

0,9*DTD' (cm)

(Equation 3.4) Danalysis (cm) Scaling Factor

Z1 0.64 18.09 17.84 20.39 15.14 1.347

Z2 0.80 22.62 22.30 25.49 19.06 1.337

Z3 1.14 32.23 31.78 36.33 26.36 1.378

Z4 1.30 36.75 36.24 41.42 36.46 1.136

Table 5.4 Calculation of scaling factor for Type-II according to IBC2000

SD1 DD (cm)

(Equation 3.1)

DD' (cm)

(Equation 3.7)

0,9*DTD' (cm)

(Equation 3.4) Danalysis (cm) Scaling Factor

Z1 0.64 24.10 23.56 26.93 21.01 1.282

Z2 0.80 30.13 29.45 33.66 26.44 1.273

Z3 1.14 42.90 41.94 47.94 36.60 1.310

Z4 1.30 48.92 47.82 54.66 50.60 1.080

Table 5.5 Calculation of scaling factor for Type-III according to IBC2000

SD1 DD (cm)

(Equation 3.1)

DD' (cm)

(Equation 3.7)

0,9*DTD' (cm)

(Equation 3.4) Danalysis (cm) Scaling Factor

Z1 0.64 31.46 27.24 31.14 28.00 1.112

Z2 0.80 39.33 34.05 38.92 35.43 1.099

Z3 1.14 56.04 48.52 55.46 48.80 1.136

Z4 1.30 63.91 55.33 63.24 67.40 no need to scale

Scaling according to FEMA-273:

When the FEMA-273 is considered, the design displacement determined by response

spectrum analysis, Danalysis, must be greater than the value of DTD prescribed by

Equation 3.4. Otherwise, all response parameters, including component actions and

deformations, must be adjusted upward proportionally to the DTD value and used for

design.

65

Table 5.6 Calculation of scaling factor for Type-I according to FEMA-273

SD1

DD (cm)

(Equation 3.1)

DTD (cm)

(Equation 3.4) Danalysis (cm) Scaling Factor

Z1 0.64 18.09 22.97 15.14 1.517

Z2 0.80 22.62 28.73 19.06 1.507

Z3 1.14 32.23 40.93 26.36 1.553

Z4 1.30 36.75 46.67 36.46 1.280

Table 5.7 Calculation of scaling factor for Type-II according to FEMA-273

SD1

DD (cm)

(Equation 3.1)

DTD (cm)

(Equation 3.4) Danalysis (cm) Scaling Factor

Z1 0.64 24.10 30.61 21.01 1.457

Z2 0.80 30.13 38.26 26.44 1.447

Z3 1.14 42.90 54.49 36.60 1.489

Z4 1.30 48.92 62.13 50.60 1.228

Table 5.8 Calculation of scaling factor for Type-III according to FEMA-273

SD1

DD (cm)

(Equation 3.1)

DTD (cm)

(Equation 3.4) Danalysis (cm) Scaling Factor

Z1 0.64 31.46 39.95 28.00 1.427

Z2 0.80 39.33 49.95 35.43 1.410

Z3 1.14 56.04 71.17 48.80 1.458

Z4 1.30 63.91 81.17 67.40 1.204

5.1.1.3 Scaling for Time History Analysis

Building Type II is analyzed with time history analysis and the results of the analysis

are scaled according to both FEMA-273 and IBC2000. The parameters needed for

the calculation of scaling factors are given below. The damping coefficient, BD, is

taken

66

as 1.38 for the calculations since the HDR, bearings designed in Section 4.1, are

used for the analysis. The fixed based, T, and isolated periods, TD, of the building are

given in Table 5.2.

Scaling according to IBC2000

The displacement dependent scaling limit for time history analysis is same with the

one given for response spectrum analysis. However, the design base shear force on

the structure above the isolation system must be greater than 60% of VS as prescribed

by Equation 3.5. Otherwise, all response parameters, including component actions

and deformations, must be adjusted proportionally upward.

When the results of the analyses are examined, it is seen that the first scaling limit,

Danalysis > 90% of DTD', is more critical than the second one and results in greater

scaling factors. Therefore, it is used in the scaling factor calculations.

Table 5.9 Calculation of scaling factor for Type-II according to IBC2000

SD1

DD (cm)

(Equation 3.1)

DD' (cm)

(Equation 3.7)

0,9*DTD' (cm)

(Equation 3.4)

Danalysis

(cm) Scaling Factor

Z1 0.64 24.10 23.56 26.93 30.80 no need to scale

Z2 0.80 30.13 29.45 33.66 30.80 1.093

Z3 1.14 42.90 41.94 47.94 30.80 1.557

Z4 1.30 48.92 47.82 54.66 30.80 1.775

Scaling according to FEMA-273

When the FEMA-273 is considered, the design displacement determined by time

history analysis, Danalysis, must be greater than the value of DD' prescribed by Equation

3.7. Otherwise, all response parameters, including component actions and

deformations, must be adjusted upward proportionally to the DD' value and used for

design.

67

Table 5.10 Calculation of scaling factor for Type-II according to FEMA-273

SD1 DD (cm)

(Equation 3.1)

DD' (cm)

(Equation 3.7) Danalysis (cm) Scaling Factor

Z1 0.64 24.10 23.56 30.80 no need to scale

Z2 0.80 30.13 29.45 30.80 no need to scale

Z3 1.14 42.90 41.94 30.80 1.362

Z4 1.30 48.92 47.82 30.80 1.553

5.1.2 Results of the Analyses

The results of the analyses of building Type-II, representing the typical symmetrical

structure, are given in Table 5.11 below; also in order to be able to compare different

analysis methods a comparison table, Table 5.12, is prepared. It can be concluded

from the comparison table that response spectrum analysis, scaled according to

FEMA-273 provisions, results in the most conservative design values.

68

Table 5.11 Results of the analyses for Type-I

T

(sec)

Base Shear in

X Direction VX (kN)

Base Shear in

Y Direction VY (kN)

Base Moment

in X Direction

MX (kN.m)

Base Moment

in Y Direction

MY (kN.m)

Max. Interstory

Drift Ratio

Max. Isolator

Displacement (cm)

Z1 1.57 4614 5160 29113 26169 0.0050 23.1

Z2 1.57 4614 5160 29113 26169 0.0050 23.1 NO

NE

ED

TO

SC

ALE

Z3 1.57 6294 7039 39651 35641 0.0070 31.4

TIM

E H

IST

OR

Y

Z4 1.57 7174 7963 45295 40715 0.0078 35.9 RE

SU

LT

S

AR

E

SC

ALE

D

Z1 1.57 5148 5147 29112 29108 0.0053 23.0

Z2 1.57 6438 6438 36408 36404 0.0066 28.7

Z3 1.57 9178 9177 51897 51891 0.0095 40.9

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 1.57 10461 10461 59155 59149 0.0108 46.7

RE

SU

LT

S A

RE

SC

ALE

D

Z1 1.57 4076 4076 27970 27970 0.0045 21.8

Z2 1.57 5093 5093 34962 34962 0.0051 25.0

Z3 1.57 7253 7253 49788 49788 0.0074 37.9

FE

MA

-273

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 1.57 8270 8270 56774 56774 0.0089 44.3

NO

NE

ED

TO

SC

ALE

Z1 1.57 4614 5160 29113 26169 0.0050 23.1

NO

NEED

TO

SCALE

Z2 1.57 5091 5696 31819 28602 0.0057 25.5

Z3 1.57 7246 8115 45328 41077 0.0081 36.3

TIM

E H

IST

OR

Y

Z4 1.57 8275 9251 51674 46830 0.0092 41.4 RE

SU

LT

S A

RE

SC

ALE

D

Z1 1.57 4571 4571 25849 25846 0.0047 20.4

Z2 1.57 5712 5712 32301 32297 0.0059 25.5

Z3 1.57 8143 8143 46049 46043 0.0084 36.3

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 1.57 9285 9284 52500 52494 0.0096 41.4

RE

SU

LT

S A

RE

SC

ALE

D

Z1 1.57 4076 4076 27970 27970 0.0045 21.8

Z2 1.57 5093 5093 34962 34962 0.0051 25.0

Z3 1.57 7253 7253 49788 49788 0.0074 37.9

IBC

2000

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 1.57 8270 8270 56774 56774 0.0089 44.3

NO

NE

ED

TO

SC

ALE

69

Table 5.12 Results of the analyses for Type-II

T

(sec)

Base Shear in

X Direction VX (kN)

Base Shear in

Y Direction VY (kN)

Base Moment

in X Direction

MX (kN.m)

Base Moment

in Y Direction

MY (kN.m)

Max. Interstory

Drift Ratio

Max. Isolator

Displacement (cm)

Z1 2.09 6156 6885 59413 53405 0.0070 30.8

Z2 2.09 6156 6885 59413 53405 0.0070 30.8 NO

NE

ED

TO

SC

ALE

Z3 2.09 8384 9377 80921 72738 0.0095 41.9

TIM

E H

IST

OR

Y

Z4 2.09 9560 10692 92268 82938 0.0109 47.8 RE

SU

LT

S

AR

E

SC

ALE

D

Z1 2.09 6868 6859 59410 59415 0.0073 30.6

Z2 2.09 8582 8572 74213 74225 0.0091 38.3

Z3 2.09 12226 12211 105702 105720 0.0129 54.5

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 2.09 13940 13923 120501 120528 0.0149 62.1

RE

SU

LT

S A

RE

SC

ALE

D

Z1 2.09 5432 5432 57081 57081 0.0062 29.0

Z2 2.09 6790 6790 71351 71351 0.0071 33.3

Z3 2.09 9670 9670 101609 101609 0.0102 50.5

FE

MA

-273

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 2.09 11027 11027 115867 115867 0.0124 59.0

NO

NE

ED

TO

SC

ALE

Z1 2.09 6156 6885 59413 53405 0.0070 30.8

NO

NEED

TO

SCALE

Z2 2.09 6729 7525 64938 58372 0.0077 33.7

Z3 2.09 9585 10720 92506 83152 0.0109 48.0

TIM

E H

IST

OR

Y

Z4 2.09 10927 12221 105458 94794 0.0124 54.7 RE

SU

LT

S A

RE

SC

ALE

D

Z1 2.09 6043 6035 52274 52279 0.0064 26.9

Z2 2.09 7550 7541 65289 65301 0.0080 33.7

Z3 2.09 10756 10743 92995 93011 0.0114 47.9

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 2.09 12260 12245 105978 106002 0.0131 54.7

RE

SU

LT

S A

RE

SC

ALE

D

Z1 2.09 5432 5432 57081 57081 0.0062 29.0

Z2 2.09 6790 6790 71351 71351 0.0071 33.3

Z3 2.09 9670 9670 101609 101609 0.0102 50.5

IBC

2000

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 2.09 11027 11027 115867 115867 0.0124 59.0

NO

NE

ED

TO

SC

ALE

70

Table 5.13 Results of the analyses for Type-III

T

(sec)

Base Shear in

X Direction VX (kN)

Base Shear in

Y Direction VY (kN)

Base Moment

in X Direction

MX (kN.m)

Base Moment

in Y Direction

MY (kN.m)

Max. Interstory

Drift Ratio

Max. Isolator

Displacement (cm)

Z1 2.73 8040 8974 119026 106886 0.0094 40.3

Z2 2.73 8040 8974 119026 106886 0.0094 40.3 NO

NE

ED

TO

SC

ALE

Z3 2.73 10949 12222 160852 145580 0.0128 54.8

TIM

E H

IST

OR

Y

Z4 2.73 12486 13936 184847 165994 0.0146 62.5 RE

SU

LT

S

AR

E

SC

ALE

D

Z1 2.73 8970 8931 118865 118915 0.0098 40.0

Z2 2.73 11223 11173 148676 148718 0.0122 50.0

Z3 2.73 15967 15893 211244 211414 0.0174 71.2

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 2.73 18225 18142 240976 241210 0.0198 81.2

RE

SU

LT

S A

RE

SC

ALE

D

Z1 2.73 7101 7101 114149 114149 0.0083 37.9

Z2 2.73 8877 8877 142686 142686 0.0095 43.2

Z3 2.73 12642 12642 203196 203196 0.0137 66.0

FE

MA

-273

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 2.73 14416 14416 231709 231709 0.0166 77.1

NO

NE

ED

TO

SC

ALE

Z1 2.73 8040 8974 119026 106886 0.0094 40.3

NO

NEED

TO

SCALE

Z2 2.73 8430 9001 121012 116057 0.0103 44.5

Z3 2.73 12007 12821 171837 164800 0.0145 63.2

TIM

E H

IST

OR

Y

Z4 2.73 13688 14616 196118 188086 0.0165 71.9 RE

SU

LT

S A

RE

SC

ALE

D

Z1 2.73 6990 6959 92626 92666 0.0076 31.1

Z2 2.73 8748 8708 115883 115916 0.0095 38.9

Z3 2.73 12441 12383 164591 164723 0.0135 55.5

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 2.73 15137 15068 200147 200341 0.0165 63.2

RE

SU

LT

S A

RE

SC

ALE

D

Z1 2.73 7101 7101 114149 114149 0.0083 37.9

Z2 2.73 8877 8877 142686 142686 0.0095 43.2

Z3 2.73 12642 12642 203196 203196 0.0137 66.0

IBC

2000

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 2.73 14416 14416 231709 231709 0.0166 77.1

NO

NE

ED

TO

SC

ALE

71

Table 5.14 Comparison Table for Type-II

(Results are scaled according to IBC2000 Time History Analysis)

T

(sec)

Base Shear in X Direction

VX (kN)

Base Shear in Y Direction

VY (kN)

Base Moment

in X Direction MX (kN.m)

Base Moment

in Y Direction MY (kN.m)

Max. Interstory Drift Ratio

Max. Isolator

Displacement (cm)

Z1 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Z2 1.00 0.91 0.91 0.91 0.91 0.91 0.91

NO

NEED

TO

SCALE

Z3 1.00 0.87 0.87 0.87 0.87 0.87 0.87

TIM

E H

IST

OR

Y

Z4 1.00 0.87 0.87 0.87 0.87 0.87 0.87 RE

SU

LT

S

AR

E

SC

ALE

D

Z1 1.00 1.12 1.00 1.00 1.11 1.04 0.99

Z2 1.00 1.28 1.14 1.14 1.27 1.19 1.14

Z3 1.00 1.28 1.14 1.14 1.27 1.18 1.14

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 1.00 1.28 1.14 1.14 1.27 1.20 1.14

RE

SU

LT

S A

RE

SC

ALE

D

Z1 1.00 0.88 0.79 0.96 1.07 0.89 0.94

Z2 1.00 1.01 0.90 1.10 1.22 0.93 0.99

Z3 1.00 1.01 0.90 1.10 1.22 0.94 1.05

FE

MA

-273

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 1.00 1.01 0.90 1.10 1.22 1.00 1.08

NO

NE

ED

TO

SC

ALE

Z1 1.00 1.00 1.00 1.00 1.00 1.00 1.00

NO

NEED

TO

SCALE

Z2 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Z3 1.00 1.00 1.00 1.00 1.00 1.00 1.00

TIM

E H

IST

OR

Y

Z4 1.00 1.00 1.00 1.00 1.00 1.00 1.00 RE

SU

LT

S A

RE

SC

ALE

D

Z1 1.00 0.98 0.88 0.88 0.98 0.91 0.87

Z2 1.00 1.12 1.00 1.01 1.12 1.05 1.00

Z3 1.00 1.12 1.00 1.01 1.12 1.05 1.00

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 1.00 1.12 1.00 1.00 1.12 1.05 1.00

RE

SU

LT

S A

RE

SC

ALE

D

Z1 1.00 0.88 0.79 0.96 1.07 0.89 0.94

Z2 1.00 1.01 0.90 1.10 1.22 0.93 0.99

Z3 1.00 1.01 0.90 1.10 1.22 0.94 1.05

IBC

2000

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 1.00 1.01 0.90 1.10 1.22 1.00 1.08

NO

NE

ED

TO

SC

ALE

72

In both IBC2000 and FEMA-273, it is mentioned that if three time history data sets

are used in the analysis of a structure, the maximum value of each response

parameter should be used to determine design acceptability; where as if seven or

more time history data sets are employed, the average value of each response

parameter is permitted to be used. As mentioned in Section 3.3.3, seven different

ground motion data sets are used in the time history analysis and average of each

design parameter is presented in Table 5.11. When the results of each time history

analysis, given in Table 5.13, are examined, one would figure out that Coyote Lake

ground motion displaces the isolators only 3.7cm. It means that the ground motion

does not impact the model structure extensively. This outcome is the expected result

of low magnitude of Coyote Lake earthquake, MW = 5.7, compared to other

earthquake data.

Table 5.15 Results of time history analysis for each earthquake record, Type-II

Site

Condition

Base Shear in

X Direction

VX (kN)

Base Shear in

Y Direction

VY (kN)

Base Moment

in X Direction MX (kN.m)

Base Moment

in Y Direction

MY

(kN.m)

Max. Interstory

Drift Ratio

Max. Isolator

Displacement (cm)

Shear Strain

(%)

DÜ

ZC

E

Soft Soil 11671 11616 99533 100423 0.0110 52.0 260

IMP

ER

IAL

V

AL

LE

Y

Soft Soil 11123 11115 96341 96020 0.0125 49.6 248

LA

ND

ER

S

Rock 3993 3958 34443 34761 0.0040 17.8 89 FA

R F

AU

LT

LO

MA

P

RIE

TA

Hard Soil 5586 5577 48423 48205 0.0057 24.9 124

CO

YO

TE

L

AK

E

Rock 836 838 7346 7256 0.0008 3.7 19

.2&$

(/ø

Rock 6578 11616 99533 56885 0.0110 51.8 259

NE

AR

FA

UL

T

SU

PE

RS

TIT

N

HIL

LS

Rock 3309 3475 30275 30284 0.0042 15.5 78

Average 6156 6885 59413 53405 0.0070 30.8 154

73

The parameters used for design purposes show great modification depending upon

the used scaling factor. The following figures are prepared to be able to comprehend

this effect. The relevant comments, in Section 5.3, on comparison of IBC2000 and

FEMA-273 are made in the light of following figures.

9[��N1�

����62,/�7<3(=� =� =� =�

%()25(�6&$/,1*6&$/,1*�:,7+�,%&����6&$/,1*�:,7+�)(0$

�����

����

����

Figure 5.1 Base shear in X direction,

(Type-II, time history analysis)

Base shear values in X direction as a function of soil types are given above in Figure

5.1. Before scaling and after scaling values are presented. As it is seen for soil type

Z1 there is no need of scaling for both methods. For Z2 type only, scaling according

to IBC2000 is needed. The significance of scaling is increased as the soil becomes

softer.

74

9\��N1�

62,/�7<3(=� =� =� =�

����

�����

�����

����

%()25(�6&$/,1*6&$/,1*�:,7+�,%&����6&$/,1*�:,7+�)(0$

����

Figure 5.2 Base shear in Y direction,

(Type-II, time history analysis)

Base shear values in Y direction as a function of soil types are given above in Figure

5.2. The similar behavior, described above for base shear in X direction, is also seen

for base shear in Y direction.

0[��N1�P�

62,/�7<3(=� =� =� =�

%()25(�6&$/,1*6&$/,1*�:,7+�,%&����6&$/,1*�:,7+�)(0$

������

�����

�����

�����

Figure 5.3 Base moment in X direction,

(Type-II, time history analysis)

75

Base moment values in X direction as a function of soil types are given above in

Figure 5.3. Before scaling and after scaling values are presented. As it is seen for soil

type Z1 there is no need of scaling for both methods. For Z2 type only, scaling

according to IBC2000 is needed. The significance of scaling is increased as the soil

becomes softer.

0\��N1�P�

62,/�7<3(=� =� =� =������

%()25(�6&$/,1*6&$/,1*�:,7+�,%&����6&$/,1*�:,7+�)(0$

�����

�����

������

Figure 5.4 Base moment in Y direction,

(Type-II, time history analysis)

Base moment values in Y direction as a function of soil types are given above in

Figure 5.4. . The similar behavior, described above for base moment in X direction,

is also seen for base moment in Y direction.

76

+K

62,/�7<3(=� =� =� =�

PD[

������

%()25(�6&$/,1*6&$/,1*�:,7+�,%&����6&$/,1*�:,7+�)(0$

������

������

������

������

Figure 5.5 Maximum interstory drift ratio,

(Type-II, time history analysis)

Maximum interstory drift ratios as a function of soil types are given above in Figure

5.5. Before scaling and after scaling values are presented. As it is seen for soil type

Z1 there is no need of scaling for both methods. For Z2 type only, scaling according

to IBC2000 is needed. The significance of scaling is increased as the soil becomes

softer.

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Figure 5.6 Base shear in X direction,

(Type-II, response spectrum analysis)

77

Base shear values in X direction as a function of soil types are given above in Figure

5.6. Before scaling and after scaling values are presented. As it is seen, the results are

scaled according to both IBC2000 and FEMA-273 for all of the soil types. The

significance of scaling does not affected by soil type except that it is decreased for

soil type Z4.

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Figure 5.7 Base shear in Y direction,

(Type-II, response spectrum analysis)

Base shear values in Y direction as a function of soil types are given above in Figure

5.7. . The similar behavior, described above for base shear in X direction, is also seen

for base shear in Y direction.

78

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Figure 5.8 Base moment in X direction,

(Type-II, response spectrum analysis)

Base moment values in X direction as a function of soil types are given above in

Figure 5.8. Before scaling and after scaling values are presented. As it is seen, the

results are scaled according to both IBC2000 and FEMA-273 for all of the soil types.

The significance of scaling does not affected by soil type except that it is decreased

for soil type Z4.

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Figure 5.9 Base moment in Y direction,

(Type-II, response spectrum analysis)

79

Base moment values in Y direction as a function of soil types are given above in

Figure 5.9. . The similar behavior, described above for base moment in X direction,

is also seen for base moment in Y direction.

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Figure 5.10Maximum interstory drift ratio,

(Type-II, response spectrum analysis)

Maximum interstory drift ratios as a function of soil types are given above in Figure

5.10. Before scaling and after scaling values are presented. As it is seen, the results

are scaled according to both IBC2000 and FEMA-273 for all of the soil types. The

significance of scaling does not affected by soil type except that it is decreased for

soil type Z4.

80

5.2 Analysis of the Base Isolated Non-symmetrical Building

To identify the effect of “scaling” phenomenon mentioned in FEMA-273 & IBC2000

and make a comparison between these two codes from the “scaling” point of view,

building Type-IV, introduced in Section 3.2.4, is analyzed. The high damping rubber

bearings, HDR, designed in Section 4.1 are used for the isolation of the buildings.

Static equivalent lateral force, response spectrum and time history analyses,

described in Sections 3.3.1, 3.3.2 and 3.3.3, are carried out on the model building

which typifies the class of non-symmetrical structure that is encountered in design.

The analyses of the isolated buildings are done for each soil type that is given in the

Turkish Seismic Code (Z1, Z2, Z3, and Z4).

5.2.1 Scaling of the Results

The results of the analyses are scaled according to both FEMA-273 and IBC2000 as

mentioned in Section 3.4. The detailed calculation of scaling factors for each analysis

method is given below.

5.2.1.1 Scaling for Static Equivalent Lateral Force Procedure

The limits of scaling mentioned in FEMA-273 and IBC2000 for static equivalent

lateral force procedure are the same except that an additional limit is also defined in

IBC2000: “The base shear must be greater than the lateral seismic force required for

a fixed-base structure of the same weight and a period equal to the isolated period”.

Building Type-IV is analyzed with static equivalent lateral force procedure and the

results of the analysis are scaled according to the mentioned limit. For the calculation

of the lateral seismic force, VT, the procedure described in Turkish Seismic Code is

used.

81

A0 = 0.40

I = 1.4

R = 8 (Seismic load reduction factor for non-isolated building)

WT = 15065 kN

TD = 1.95 sec.

Table 5.16 Calculation of scaling factor for Type-IV according to IBC2000

S(T)

A(T)

(Equation 5.2)

VT (kN)

(Equation 5.1)

VS (kN)

(Equation 3.5) Scaling Factor

Z1 0.559 0.313 590 3985

no need to scale

Z2 0.704 0.394 743 4977

no need to scale

Z3 0.974 0.545 1028 7084

no need to scale

Z4 1.347 0.754 1421 8094

no need to scale

5.2.1.2 Scaling for Response Spectrum Analysis

Building Type IV is analyzed with response spectrum analysis and the results of the

analysis are scaled according to both FEMA-273 and IBC2000. To be

comprehendible, the parameters needed for the calculation of scaling factors are

given below. The damping coefficient, BD, is taken as 1.38 for the calculations since

the HDR, bearings designed in Section 4.1, are used for the isolation. As a result of

the modal analysis the fixed based, T, and isolated periods, TD, of the building are

determined as:

Table 5.17 Fixed and isolated periods

Type-IV

T (sec.) 0.43

TD (sec.) 1.95

82

Scaling according to IBC2000:

When the IBC2000 is considered, the design displacement determined by response

spectrum analysis, Danalysis, must be greater than 90% of DTD' as specified in Equation

3.4. On the other hand, the design base shear force on the structure above the

isolation system must be greater than VS as prescribed by Equation 3.5. Otherwise,

all response parameters, including component actions and deformations, must be

adjusted proportionally upward.

When the results of the analyses are examined, it is seen that the first scaling limit,

Danalysis > 0.9×DTD', is more critical than the second one and results in greater scaling

factors. Therefore, displacement dependent scaling limit is used in the scaling factor

calculations.

Table 5.18 Calculation of scaling factor for Type-IV according to IBC2000

SD1 DD (cm)

(Equation 3.1)

DD' (cm)

(Equation 3.7)

0,9*DTD' (cm)

(Equation 3.4) Danalysis (cm)

Scaling

Factor

Z1 0.64 22.50 22.00 25.15 20.73 1.213

Z2 0.80 28.10 27.40 31.32 26.10 1.200

Z3 1.14 40.00 39.10 44.69 36.08 1.239

Z4 1.30 45.70 44.60 50.98 49.91 1.021

Scaling according to FEMA-273:

When the FEMA-273 is considered, the design displacement determined by response

spectrum analysis, Danalysis, must be greater than the value of DTD prescribed by

Equation 3.4. Otherwise, all response parameters, including component actions and

deformations, must be adjusted upward proportionally to the DTD value and used for

design.

83

Table 5.19 Calculation of scaling factor for Type-IV according to FEMA-273

SD1

DD (cm)

(Equation 3.1)

DTD (cm)

(Equation 3.4) Danalysis (cm) Scaling Factor

Z1 0.64 22.50 28.58 20.73 1.378

Z2 0.80 28.10 35.69 26.10 1.367

Z3 1.14 40.00 50.80 36.08 1.408

Z4 1.30 45.70 58.04 49.91 1.163

5.2.1.3 Scaling for Time History Analysis

Building Type IV is analyzed with time history analysis and the results of the

analysis are scaled according to both FEMA-273 and IBC2000. The parameters

needed for the calculation of scaling factors are given below. The damping

coefficient, BD, is taken as 1.38 for the calculations since the HDR, bearings

designed in Section 4.1, are used for the analysis. The fixed based, T, and isolated

periods, TD, of the building are as given in Table 5.15.

Scaling according to IBC2000

The displacement dependent scaling limit for time history analysis is same with the

one given for response spectrum analysis. However, the design base shear force on

the structure above the isolation system must be greater than 80% of VS as prescribed

by Equation 3.5. Otherwise, all response parameters, including component actions

and deformations, must be adjusted proportionally upward.

When the results of the analyses are examined, it is seen that the first scaling limit,

Danalysis > 0.9×DTD', is more critical than the second one and results in greater scaling

factors. Therefore, it is used in the scaling factor calculations.

84

Table 5.20 Calculation of scaling factor for Type-IV according to IBC2000

SD1

DD (cm)

(Equation 3.1)

DD' (cm)

(Equation 3.7)

0,9*DTD' (cm)

(Equation 3.4) Danalysis (cm) Scaling Factor

Z1 0.64 22.50 22.00 25.15 30.70 no need to scale

Z2 0.80 28.10 27.40 31.32 30.70 1.020

Z3 1.14 40.00 39.10 44.69 30.70 1.456

Z4 1.30 45.70 44.60 50.98 30.70 1.661

Scaling according to FEMA-273

When the FEMA-273 is considered, the design displacement determined by time

history analysis, Danalysis, must be greater than the value of DD' prescribed by Equation

3.7. Otherwise, all response parameters, including component actions and

deformations, must be adjusted upward proportionally to the DD' value and used for

design.

Table 5.21 Calculation of scaling factor for Type-IV according to FEMA-273

SD1 DD (cm)

(Equation 3.1)

DD' (cm)

(Equation 3.7) Danalysis (cm) Scaling Factor

Z1 0.64 22.50 22.00 30.70 no need to scale

Z2 0.80 28.10 27.40 30.70 no need to scale

Z3 1.14 40.00 39.10 30.70 1.27

Z4 1.30 45.70 44.60 30.70 1.45

5.2.2 Results of the Analyses

The results of the analyses of building Type-IV, representing the typical non-

symmetrical structure, are given in Table 5.20 below; also in order to be able to

compare different analysis methods a comparison table, Table 5.21, is prepared. It

can be concluded from the comparison table that response spectrum analysis, scaled

according to FEMA-273 provisions, results in the most conservative design values.

85

Table 5.22 Results of the analyses for Type-IV

T

(sec)

Base Shear in

X Direction VX (kN)

Base Shear in

Y Direction VY (kN)

Base Moment

in X Direction

MX

(kN.m)

Base Moment

in Y Direction

MY

(kN.m)

Rotational Moment

Mz (kN.m)

Max. Interstory

Drift Ratio

Max. Isolator

Disp. (cm)

Z1 1.95 4485 5040 41153 36253 20350 0.0070 30.7

Z2 1.95 4485 5040 41153 36253 20350 0.0070 30.7

NO

NE

ED

TO

SC

ALE

Z3 1.95 5696 6401 52264 46041 25845 0.0089 39.0

TIM

E H

IST

OR

Y

Z4 1.95 6503 7308 59672 52567 29508 0.0102 44.5 RE

SU

LT

S

AR

E

SC

ALE

D

Z1 1.95 4656 4627 41312 41459 19400 0.0066 28.6

Z2 1.95 5815 5780 51581 51768 24234 0.0082 35.7

Z3 1.95 8282 8231 73426 73698 34510 0.0117 50.8

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 1.95 9463 9405 83890 84201 39435 0.0134 58.0

RE

SU

LT

S

AR

E

SC

ALE

D

Z1 1.95 3985 3985 43835 43835 14784 0.0055 33.4

Z2 1.95 4977 4977 54747 54747 18465 0.0069 41.6

Z3 1.95 7084 7084 77924 77924 26282 0.0099 59.1

FE

MA

-273

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 1.95 8094 9084 89034 89034 33702 0.0114 67.6

NO

NE

ED

TO

SC

ALE

Z1 1.95 4485 5040 41153 36253 20350 0.0070 30.7

NO

NEED

TO

SCALE

Z2 1.95 4575 5141 41976 36978 20757 0.0071 31.3

Z3 1.95 6530 7338 59919 52784 29630 0.0102 44.7

TIM

E H

IST

OR

Y

Z4 1.95 7450 8371 68355 60216 33801 0.0116 51.0

RE

SU

LT

S

AR

E

SC

ALE

D

Z1 1.95 4098 4073 36366 36494 17077 0.0058 25.2

Z2 1.95 5105 5074 45280 45444 21273 0.0072 31.3

Z3 1.95 7288 7243 64613 64852 30368 0.0103 44.7

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 1.95 8308 8257 73647 73920 34620 0.0117 51.0

RE

SU

LT

S

AR

E

SC

ALE

D

Z1 1.95 3985 3985 43835 43835 14784 0.0055 33.4

Z2 1.95 4977 4977 54747 54747 18465 0.0069 41.6

Z3 1.95 7084 7084 77924 77924 26282 0.0099 59.1

IBC

2000

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 1.95 8094 9084 89034 89034 33702 0.0114 67.6

NO

NE

ED

TO

SC

ALE

86

Table 5.23 Comparison Table for Type-IV

(Results are scaled according to IBC2000 Time History Analysis)

T

(sec)

Base Shear in

X Direction VX (kN)

Base Shear in

Y Direction VY (kN)

Base Moment

in X Direction

MX

(kN.m)

Base Moment

in Y Direction

MY

(kN.m)

Rotational Moment

Mz

(kN.m)

Max. Interstory

Drift Ratio

Max. Isolator

Disp. (cm)

Z1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Z2 1.00 0.98 0.98 0.98 0.98 0.98 0.98 0.98

Z3 1.00 0.87 0.87 0.87 0.87 0.87 0.87 0.87

TIM

E H

IST

OR

Y

Z4 1.00 0.87 0.87 0.87 0.87 0.87 0.87 0.87

Z1 1.00 1.04 0.92 1.00 1.14 0.95 0.94 0.93

Z2 1.00 1.27 1.12 1.23 1.40 1.17 1.15 1.14

Z3 1.00 1.27 1.12 1.23 1.40 1.16 1.15 1.14

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 1.00 1.27 1.12 1.23 1.40 1.17 1.15 1.14

Z1 1.00 0.89 0.79 1.07 1.21 0.73 0.79 1.09

Z2 1.00 1.09 0.97 1.30 1.48 0.89 0.97 1.33

Z3 1.00 1.08 0.97 1.30 1.48 0.89 0.97 1.32

FE

MA

-273

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 1.00 1.09 1.09 1.30 1.48 1.00 0.98 1.33

Z1 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Z2 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Z3 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

TIM

E H

IST

OR

Y

Z4 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Z1 1.00 0.91 0.81 0.88 1.01 0.84 0.83 0.82

Z2 1.00 1.12 0.99 1.08 1.23 1.02 1.01 1.00

Z3 1.00 1.12 0.99 1.08 1.23 1.02 1.01 1.00

RE

SP

ON

SE

S

PE

CT

RU

M

Z4 1.00 1.12 0.99 1.08 1.23 1.02 1.01 1.00

Z1 1.00 0.89 0.79 1.07 1.21 0.73 0.79 1.09

Z2 1.00 1.09 0.97 1.30 1.48 0.89 0.97 1.33

Z3 1.00 1.08 0.97 1.30 1.48 0.89 0.97 1.32

IBC

2000

EQ

UIV

AL

EN

T

LA

TE

RA

L

Z4 1.00 1.09 1.09 1.30 1.48 1.00 0.98 1.33

87

In both IBC2000 and FEMA-273, it is mentioned that the selected ground motion

sets for time history analysis must have magnitude, fault distance and source

mechanism that are equivalent to design earthquake ground motion. The results of

each time history analysis are given in Table 5.12 and Table 5.22 for five-storey

symmetrical, Type-II, and non-symmetrical, Type-IV, building types respectively.

When the results are examined; it is clear that in addition to the magnitude, fault

distance and source mechanism, also the conditions of site where earthquake data is

recorded have a great influence on the results. As the soil where the ground motion

data is recorded, becomes softer the response of the structure increases. Therefore

when selecting a ground motion data set, site condition must be also taken into

account in addition. When the results of each time history analysis, given in Table

5.22, are examined, one would figure out that Coyote Lake ground motion displaces

the isolators only 4.0cm. It means that the ground motion does not impact the model

structure extensively. This outcome is the expected result of low magnitude of

Coyote Lake earthquake, MW = 5.7, compared to other earthquake data.

Table 5.24 Results of time history analysis for each earthquake record, Type-IV

Site

Condition

Base Shear in X

Direction VX (kN)

Base Shear in Y

Direction VY (kN)

Base Moment

in X Direction

MX

(kN.m)

Base Moment

in Y Direction

MY

(kN.m)

Max. Interstory

Drift Ratio

Max. Isolator

Disp. (cm)

Shear Strain

(%)

DÜZCE Soft Soil 8573 8441 75537 76913 0.0102 52.8 264

IMPERIAL VALLEY Soft Soil 7692 7684 42263 42253 0.0121 44.8 224

LANDERS Rock 3863 3804 33875 34130 0.0057 22.6 113

FA

R F

AU

LT

LOMA PRIETA

Hard

Soil 3182 3254 29036 28425 0.0053 19.7 99

COYOTE LAKE Rock 699 693 5747 6661 0.0009 4.0 20

.2&$(/ø Rock 4399 8441 75537 39024 0.0101 52.8 264

NE

AR

FA

UL

T

S. HILLS Rock 2990 2961 26075 26368 0.0046 17.9 90

Average 4485 5040 41153 36253 0.0070 30.7 154

88

The following figures are prepared to be able to comprehend scaling effect. The

relevant comments, in Section 5.3, on comparison of IBC2000 and FEMA-273 are

made in the light of following figures.

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Figure 5.11 Base shear in X direction,

(Type-IV, time history analysis)

Base shear values in X direction as a function of soil types are given above in Figure

5.11. Before scaling and after scaling values are presented. As it is seen for soil type

Z1 there is no need of scaling for both methods. For Z2 type only, scaling according

to IBC2000 is needed. The significance of scaling is increased as the soil becomes

softer.

89

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Figure 5.12 Base shear in Y direction,

(Type-IV, time history analysis)

Base shear values in Y direction as a function of soil types are given above in Figure

5.12. . The similar behavior, described above for base shear in X direction, is also

seen for base shear in Y direction.

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Figure 5.13 Base moment in X direction,

(Type-IV, time history analysis)

90

Base moment values in X direction as a function of soil types are given above in

Figure 5.13. Before scaling and after scaling values are presented. As it is seen for

soil type Z1 there is no need of scaling for both methods. For Z2 type only, scaling

according to IBC2000 is needed. The significance of scaling is increased as the soil

becomes softer.

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Figure 5.14 Base moment in Y direction,

(Type-IV, time history analysis)

Base moment values in Y direction as a function of soil types are given above in

Figure 5.14. . The similar behavior, described above for base moment in X direction,

is also seen for base moment in Y direction.

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Figure 5.15 Maximum interstory drift ratio,

(Type-IV, time history analysis)

91

Maximum interstory drift ratios as a function of soil types are given above in Figure

5.15. Before scaling and after scaling values are presented. As it is seen for soil type

Z1 there is no need of scaling for both methods. For Z2 type only, scaling according

to IBC2000 is needed. The significance of scaling is increased as the soil becomes

softer.

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Figure 5.16 Base shear in X direction,

(Type-IV, response spectrum analysis)

Base shear values in X direction as a function of soil types are given above in Figure

5.16. Before scaling and after scaling values are presented. As it is seen, the results

are scaled according to both IBC2000 and FEMA-273 for all of the soil types. The

significance of scaling does not affected by soil type except that it is decreased for

soil type Z4.

92

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Figure 5.17 Base shear in Y direction,

(Type-IV, response spectrum analysis)

Base shear values in Y direction as a function of soil types are given above in Figure

5.17. . The similar behavior, described above for base shear in X direction, is also

seen for base shear in Y direction.

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Figure 5.18 Base moment in X direction,

(Type-IV, response spectrum analysis)

93

Base moment values in X direction as a function of soil types are given above in

Figure 5.18. Before scaling and after scaling values are presented. As it is seen, the

results are scaled according to both IBC2000 and FEMA-273 for all of the soil types.

The significance of scaling does not affected by soil type except that it is decreased

for soil type Z4.

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Figure 5.19 Base moment in Y direction,

(Type-IV, response spectrum analysis)

Base moment values in Y direction as a function of soil types are given above in

Figure 5.19. . The similar behavior, described above for base moment in X direction,

is also seen for base moment in Y direction.

94

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Figure 5.20 Maximum interstory drift ratio,

(Type-IV, response spectrum analysis)

Maximum interstory drift ratios as a function of soil types are given above in Figure

5.20. Before scaling and after scaling values are presented. As it is seen, the results

are scaled according to both IBC2000 and FEMA-273 for all of the soil types. The

significance of scaling does not affected by soil type except that it is decreased for

soil type Z4.

5.3 Comparison of FEMA-273 and IBC2000

When the results of the analyses, which are given in Figures 5.1 through 5.20, are

studied; one would figure out that the codes FEMA-273 and IBC2000 give different

results for the same analysis method. The reason for this variation mainly depends on

the difference in the accepted provisions for scaling of the analysis results. Below,

the comparison of the scaling provisions, recommended in FEMA-273 and IBC2000,

is done for each method used in the analysis.

95

5.3.1 Equivalent Lateral Load Analysis

It can be seen from the Tables 5.11 & 5.20 that IBC2000 and FEMA-273 gives

identical results since the results are not needed to be scaled.

5.3.2 Response Spectrum Analysis

FEMA-273 gives more critical values for the design when response spectrum

analysis is considered. The reason depends on the difference between the accepted

scaling thresholds, which are defined in FEMA-273 and IBC2000.

While IBC2000 takes 0.9×DTD' as limit for scaling, FEMA-273 takes DTD. If the

equation for DTD', Equation 3.7, is examined; it is realized that the inequality of

“0.9×DTD' < DTD” is always valid, Therefore it is concluded that FEMA-273 is more

conservative than IBC2000 when response spectrum analysis is concerned.

The scaling factors for response spectrum analyses are given in Tables 5.3-8, 5.16-

17. When these tables are examined, it is realized that the scaling factors for each soil

type are nearly constant, very close to each other, and do not fluctuate much for

different soil types except soil type Z4. Actually, this is the expected trend since the

effect of site condition on the scaling factor is already taken into account by

assigning different spectrum functions for each soil type.

In FEMA-273 and IBC2000 site classes are categorized into six different groups as

A, B, C, D, E and F. On the other hand, in Turkish Seismic Code site classes are

grouped as Z1, Z2, Z3 and Z4. Although these groups do not match with each other

exactly, for the determination of scaling factors, it is assumed that A stands for Z1, B

stands for Z2, C stands for Z3 and D stands for Z4. The decrease in the scaling

factor for soil type Z4 when compared with Z1, Z2 and Z3 basically results from this

assumption. Because, Z4 is assumed to be identical with site class D for the analyses,

however it represents weaker soil conditions and stands for somewhere between site

96

classes D, E and F. Consequently, scaling factor Z4 decreases when compared with

Z1, Z2 and Z3.

5.3.3 Time History Analysis

The scaling limits for the time history analysis are:

Danalysis > DD' (FEMA-273)

Danalysis > 0.9 x DTD' (IBC2000)

Which one of these limits is more conservative? In order to answer this question the

applied earthquake direction must be checked.

When the Earthquake is applied in Short Direction:

If the following inequality is correct then IBC2000 is more conservative.

DD' < (0.9 x DTD')

DD' < 0.9 * DD'

++

22

121

db

ey

1.10 <

++

22

121

db

ey where;

b > d

e = 0.05 * b (5% min. eccentricity)

y = b/2

1.10 <

+∗

+=

+

∗∗∗+

)(

)3.0(1

)(

)05.012(

21

22

2

22db

b

db

bb

97

3

1<

)(22

2

db

b

+

2

d < 2

2 b∗

This inequality is always valid since b > d. Therefore, the expression of DD' < (0.9 x

DTD') is always true when earthquake is assumed to apply in short direction.

When the Earthquake is applied in Long Direction:

If the following inequality is correct then IBC2000 is more conservative.

DD' < (0.9 x DTD')

DD' < 0.9 * DD'

++

22

121

db

ey

1.10 <

++

22

121

db

ey where;

b > d

e = 0.05 * d (5% min. eccentricity)

y = d/2

1.10 <

+∗

+=

+

∗∗∗+

)(

)3.0(1

)(

)05.012(

21

22

2

22db

d

db

dd

3

1<

)(22

2

db

d

+

2

b < 2

2 d∗

98

It can be commented that for time history analysis IBC2000 is more conservative

when 2 d > b > d. So it might seem that conservativeness of IBC2000 depends on

the plan dimensions of the isolated building. However, IBC2000 states that DTD can

not be less than 1.1 times DD. So;

1.10 <

++

22

121

db

ey

is always true no matter what the plan dimensions are. Then IBC2000 is always more

conservative than FEMA-273 when time history analysis is concerned.

The scaling factors for time history analyses are given in Tables 5.9-10 and 5.18-19.

When these tables are examined, it is seen that the scaling factor increases as the site

condition worsen.

99

CHAPTER 6

CONCLUSION

In this study, the design of seismic isolation systems is explained and the influence of

base isolation on the response of structure is examined in details. Various types of

isolators are introduced and one of the most commonly used type, high damping

rubber bearing, is used in the case studies. Both alternatives of modeling an isolator

for design purposes, linear and bi-linear, are discussed; also advantages and

disadvantages of them are stated. The analyses of isolated buildings, symmetrical and

non-symmetrical in plan, are performed according to the related chapters of the

design codes FEMA and IBC2000. According to these analyses, the codes are

compared for each type of analysis method.

In the light of the results obtained from the case studies, the following conclusions

can be stated:

o The assumed equivalent linear model of isolators which is accepted by the

FEMA and IBC2000 design codes; underestimates the peak superstructure

acceleration and overestimates the bearing displacement when compared to

the bilinear model.

o For the bilinear model isolators with the increase in isolator yield

displacement, Dy, the bearing displacement also increases.

100

o When time history analysis is used, the site condition where earthquake data

is recorded has a great influence on the design parameters of the structure.

That is as the soil becomes softer, the response of the structure increases.

Therefore the selected ground motion data sets for time history analysis must

have been recorded on similar soil condition with the site where the structure

is located. It means that site condition must be also taken into account in

addition to the mentioned parameters in IBC2000 and FEMA (fault distance,

magnitude and source mechanism type).

o When compared with IBC2000, FEMA gives more critical values for the

design if response spectrum analysis is used. The reason depends on the

difference between the accepted scaling limits in FEMA and IBC2000.

o When compared with FEMA, IBC2000 gives more critical values for the

design if time history analysis is used. The reason depends on the difference

between the accepted scaling limits in FEMA and IBC2000.

o The scaling factor for response spectrum analysis does not change for

different site conditions except for soil type Z4. The decrease in the scaling

factor for soil type Z4 when compared with Z1, Z2 and Z3 basically results

from the differences between the defined site conditions in IBC2000, FEMA

and Turkish Seismic Code.

o The scaling factor for time history analyses increases as the site condition

worsen.

101

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